text:
Update: Another brand of frozen mixed berries has been recalled.
A second brand of frozen mixed berries has been withdrawn from supermarket shelves across the country, as five cases of hepatitis A linked to the product are confirmed in New South Wales and Victoria.
One-kilogram bags of Nanna's frozen mixed berries were recalled on Saturday as a result of the health scare.
The recall has now been extended to Creative Gourmet mixed berries in 300 gram and 500 gram packets.
Health officials have confirmed three cases of hepatitis A linked to the product in Victoria and two in New South Wales.
Consumers have also been told not to eat fruit from the Nanna's one-kilogram packets with best-before dates up to and including November 22, 2016.
People have also been told not to consume fruit from the Creative Gourmet 300 gram packets with best-before dates up to and including December 10, 2017, and 500 gram packets with best-before dates up to October 6, 2017.
The berries came from China and Chile and were distributed by Patties Foods, which is based in Bairnsdale, east Victoria.
Previously, Mamamia reported…
One-kilogram bags of Nanna's frozen mixed berries are being pulled off supermarket shelves across Australia because of a link to the virus Hepatitis A.
A spokesperson for the Victorian Health Department said anyone who had bought the berries was advised to immediately throw them away.
Stores are being advised and there will be advertisements in national newspapers on Monday.
For more: Raw milk recalled after death of 3 year old.
The company is fully cooperating with the recall.
Nanna's Frozen berries recalled after links to Hepatitis A. (Image ABC)
The frozen mixed berries are sold mainly in Woolworths, Coles and IGA supermarkets.
Hepatitis A is spread when traces of faecal matter containing the virus contaminate hands, objects, water or food.
Read more: When food is a killer.
The berries came from China and Chile and were packed at Patties, a company based at Bairnsdale, in eastern Victoria.
The company has been contacted for comment.
Berries the 'only link' between cases of Hepatitis A
Dr Rosemary Lester, the state's chief health officer, said frozen berries had been implicated in past outbreaks of Hepatitis A.
"Hepatitis A virus infection is uncommon and normally associated with travel to countries affected by endemic Hepatitis A," she said.
"The only common link between the cases is consumption of this product. There is no overseas travel or common restaurant exposure.
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"Sampling of the product will be undertaken to identify the virus but it is difficult to find Hepatitis A virus, even in a contaminated batch."
Dr Finn Romanes, from the Victorian Health Department, said they were asking people who had eaten this product in the past 50 days to look out for symptoms of the disease.
People who have eaten the berries in the last 50 days should look out for symptoms.
"Symptoms typically begin with fever, loss of appetite and nausea, and can progress to jaundice, which is dark urine, yellowing of the eyes," he said.
"In a very small number of cases there can be death associated with Hepatitis A infection.
"If you develop any symptoms after consuming these berries, please contact your GP."
The berries have a two-year shelf life and any product purchased from October 2014 onwards should be thrown out.
"The company's working with us to recall any product that's on the shelves of this line at all," Dr Romanes said.
"We're really asking people to be vigilant for symptoms for quite a long period because it can take up to a month or 50 days to develop symptoms."
Hospital listeria threat in mousse supplied to hospitals
In a seperate recall a number of hospitals have been told to throw out a chocolate mousse product, found in routine tests, to contain listeria.
Dear Premiers: You're gambling with babies' lives.
The mousse, which had a use-by date of February 14, 2015, was supplied to the Austin Hospital, St Vincent's Private, St Vincent's Mercy, Brunswick Private, the Royal Children's Hospital, Ballarat Health Services, Caulfield Hospital, Sandringham Hospital, Frankston Hospital and Rosebud Hospital.
No cases have been reported, but symptoms can take up to 70 days to appear.
Most healthy people are not affected by listeria or show only minor symptoms.
"The issue with listeria is that it's it's an issue for people with compromised immune systems because they can become more unwell," Dr Romanes said.
"As many people may know, some ready-to-eat foods and other foods that can contain listeria are dangerous for pregnant women their unborn babies and the elderly."
The hospitals are notifying patients who may have consumed the mousse between January 29 and February 10.
"Hospitals are taking action to contact people and there hasn't been anyone with illness identified so far," Dr Romanes said.
This article was originally published by the ABC. It has been republished here with full permission.
current-affairs
Icepax Knight 7 years ago
We have suffered problems with products manufactured or packaged in China and now it looks like our Australian friends are going through the same thing. China have been linked with various poisonous chemicals found in food or other merchandise produced, made or packaged in China. Formaldehyde found in packaged food, melamine and leather-hydrolyzed in milk and other drinking liquid, isocarbophos in packaged beans, sodium nitrite and urea in vegetables, clenbuterol used in pork production, organophosphate insecticide in cans of ham, cadmium in rice, dimethyl fumarate in sofas produced by Chinese manufacturer Linkwise, human feces used as fertilizer, and the list go on. You get the idea. Products (food, furniture, etc) made, manufactured, or packaged in China should be BANNED everywhere in the world because they are POISONING US.
SAY NO to Chinese products if you value the safety of yourself and your family.
Worried 7 years ago
I feel so worried. I'm 23 weeks pregnant. I was using these berries every day in a smoothie. One day I got gastro so bad I had to go to hospital. What if it was because of the berries? How do I know if my growing baby is going okay?


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NEXT: Tech That Generates Fake News
David Staley
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The new ambassador to the Netherlands, Peter Hoekstra, was asked by Dutch interviewers recently to clarify statements he had made in 2015 that Dutch cities were in chaos because of "the Islamic movement."
"There are cars being burned. There are politicians that are being burned…And yes, there are no-go zones in the Netherlands," he told a conservative group. (None of this is true, of course.)
Hoekstra has attempted to deflect the controversy away, largely by ignoring any such questions, and has made no effort to retract or otherwise correct his statement. Indeed, finally, Hoekstra denied having made the statements, calling the reports that he had "fake news."
As you might guess, YouTube and other outlets very quickly shared video footage of Hoekstra making precisely those statements. In an era of the rapid, viral spread of media, it should be fairly easy to discredit claims of "fake news" by hapless public figures.
If some new technologies are permitted to develop, however, it will very soon become next to impossible to use video to verify or refute such claims. Baidu—China's answer to Google—has recently announced a new app that can mimic any voice in a manner of minutes. Another company, Lyrebird, has developed a tool that can mimic any voice, and for demonstration purposes recreated the voices of Trump and Obama. The artificial intelligence behind these applications is reaching the stage where they can quickly and convincingly impersonate anyone.
Face2Face is an application that alters video footage. Imagine a video headshot of Urban Meyer taken from a press conference. Face2Face's application employs a depth-sensing camera: I would train the camera on my own face and start making funny faces or twisting my mouth in odd ways.
The application combines both my facial distortions with Urban Meyer's face to produce a composite such that Meyer appears to make strange facial contortions. I could, of course, have the depth-sensing camera record me moving my lips and saying "Michigan is a far superior team to Ohio State. I don't see how we will be able to win this season." Meyer could be convincingly made to be mouthing these words. As a public figure, Urban Meyer has a voice that's easy to capture, and after a minute or two I could use Lyrebird or some other technology to create a video of Urban Meyer conceding victory to Michigan.
Now imagine that video going viral. On the one hand, Meyer could be made to look ridiculous. He could, like Peter Hoekstra, deny ever having made that statement at all. Then, of course, people would point out the "obvious" video evidence of him making this statement. Meyer's protests would look pathetic in the face of such "evidence."
Our society would quickly descend, however, into one where no one would be able to trust "evidence," video or otherwise. Once consumer-grade versions of facial and voice mimicry become widely available, there would be little reason to believe any video or audio recordings as truthful. Of course, we might just as likely choose to believe any such fake video that confirms our beliefs and prejudices.
How would we discern falsehood from truth when the AI-enhanced technologies make such convincing fakes? How would we know that the video we are watching of the president isn't some crafty manipulation? We have already seen Hollywood insert virtual actors into movies: Peter Cushing—who died 20 years earlier–featured in Star Wars: Rogue 1. Indeed, we should expect to see many more deceased actors resurrected on film.
Using Face2Face or similar technologies, someone like Steven Colbert will mock the President in ways that won't require him to create a "Cartoon President." We might have some assurance that, because he is a satirist, the video we are seeing is probably a fake, and that that is part of the humor. To employ facial/voice mimicry in a satirical fashion will require that viewers exhibit some very educated and discerning viewership to read those larger contextual clues around video recreations. Given how susceptible people are to believing the Photoshopped forgeries spreading virally today, I am not optimistic this will happen, and decontextualized doctored videos will proliferate.
Early press reports extolled the virtues of Lyrebird's application, noting that a user could alter the voice of the narrator of an audiobook to one of their favorite actors, or customize the voice of a personal assistant. That is, rather than Alexa's voice or Siri's voice, you could create a voice of your choosing.
There is a certain "creep factor" here, of course: that recreated personal assistant's voice could be one you've captured from the person you are stalking. After a minute of recording their voice, you could be regularly conversing with and hearing the voice of your "unrequited love." I shudder at this new kind of invasion of privacy. Actors are seeking intellectual property protections of their voices and likenesses: will ordinary citizens similarly seek such protections? My voice and likeness are my property after all…right?
I bring up the creep factor here to make a more important point about facial/voice mimicry: what problem are these technologies solving? Ideally, we develop new technologies to solve a problem, understanding of course that new problems are a possible side-effect of any technological development.
It is a common refrain that "technologies are just neutral tools. It is the use that people put them to that are either good or bad." That is true, I think, for some technologies, but this is certainly not true of all technologies. I instruct my history students that the guillotine was a technology that was developed for one purpose: to kill many people more quickly and efficiently than an executioner's sword. To say that the guillotine was "just a tool" or was "neutral" until it fell into either the right or wrong hands is laughable: no one used that technology to chop lettuce or lumber. The tool was not neutral, it was designed to kill people.
What problem do technologies like Lyrebird and its ilk solve? Is it really a problem that I can't personalize my virtual assistant? Not hearing Samuel L. Jackson read my audiobook is a problem? I would contend that Lyrebird and Face2Face have been designed to create falsehoods.
David Staley is interim director of the Humanities Institute and a professor at The Ohio State University. He is president of Columbus Futurists and host of CreativeMornings Columbus.
The next Columbus Futurists monthly forum will be Thursday, March 22 at 7:30 p.m. at Ohio State's Thompson Library, Room 165. The topic for the evening will be "Continuing the Sustainability Conversation: Discounting the Future."
The next CreativeMornings Columbus will be Friday, March 16 at 8:30 a.m. at Pat and Gracie's. Sandra Lopez will speak on the theme "Courage."
David Staley is president of Columbus Futurists and a professor of history, design and educational studies at The Ohio State University. He is the host of CreativeMornings Columbus.
David Staley , face2face , fake news , futurism , futurists , lyrebird , NEXT , science , technology
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Each day patients ask me to avoid taking dental x-rays and help minimize their exposure to radiation. Rightfully so. No one wants to get their head zapped unless it's absolutely necessary. The purpose of this blog is not to discuss the consequences of radiation and x-rays. There is plenty of information out there. I am not going to discuss the harm or side effects either. We will agree that dental x-rays are definitely something we all would prefer avoiding. Rather, let's take this discussion into a new direction: What steps can be taken to minimize my dental x-ray radiation exposure?
Another helpful technique is using a lead apron with a thyroid collar. Every time a dentist takes an x-ray they cover you with a heavy blanket called a lead apron. The purpose is to block the x-ray beam from radiating the rest of your body. Please make sure your dentist uses one that covers your neck as well. There are vital organs there such as your thyroid gland and there is no need to have that area exposed. It is not enough for the apron to simply cover your upper body. The collar at the top of the apron is a simple must that will really protect you.
A final technique that I really love is spreading out the radiation over a few appointments. Simply put, taking a few today and a few tomorrow is always better than taking them all today. If you generally don't get many cavities to begin with, ask your dentist to spread out your necessary x-rays over a few appointments. This is especially useful when it's time for your six month check-ups. Oftentimes, patient's say "Doc can we skip it this time?" In reality, if you need four x-rays, you're better off taking two today and two more in six months. It's okay to have such discussions with your dentist. After all it's your body and we are here to help.
Hope this helps and feel free to contact me with any questions.
We take pride in delivering ethical, consistent, & courteous service to each & every patient.
Copyright © 2019. Love Our Dentist. All Rights Reserved.


STULZ announced the launch of its STULZ Explorer WSW water cooled chiller. This flexible chiller unit is designed for use in a diverse range of mission critical indoor applications including data centres, communications rooms, industrial and commercial buildings, and telecommunications equipment centres.
Flexibility has been designed into every aspect of the STULZ Explorer WSW and it has big cooling power in a small footprint. Depending on the required cooling capacity, the Explorer WSW chillers can be equipped with either one compressor offering a cooling capacity of 230-430kW, or two compressors that provide 460-1530kW. Further enhancing its ease of use, it can be easily adjusted to different heat loads thanks to its two refrigerant circuits with semi-hermetic screw compressors and infinitely variable output sliders.
The Explorer WSW features standardised components including shell and tube condensers that can be set to operate at different temperature levels, for example, with well water, cooling towers or external recooling heat exchangers. The evaporation process in the refrigerant circuit is controlled by electronic expansion valves, which use pressure sensors, temperature sensors and the STULZ C2020 controller to optimise heat exchange between the refrigerant and chilled water in the evaporator.
Following customer consultation, STULZ identified clear demand for a compact, corrosion resistant device that emitted low levels of noise. These features are encapsulated in the Explorer WSW and for noise critical applications a version is available that has extra acoustic insulation that meets the sound power level requirements of ISO 3744 and reduces them by a further 10dB.
Thanks to its versatility, this latest innovation from STULZ also has high efficiency in partial load mode. Depending on the service conditions, it can offer European Seasonal Energy Efficiency Ratio (ESEER) values of five or higher and also offers a variety of options such as automatic transfer switch, an energy meter for measuring total power consumption, soft start and anti-vibration mounts.


text:
One week after Hurricane Matthew, at least 300 schools damaged in Haiti, over 100,000 children miss out on learning
Download new photos and broll from: http://weshare.unicef.org/Package/2AMZIFM2233
PORT-AU-PRINCE/NEW YORK, 10 October 2016 – One week after Hurricane Matthew slammed into Haiti, and as schools re-open across the country, more than 100,000 children will be missing out on learning after their schools were either damaged or converted into shelters.
"At least 100,000 children today will not experience the joy, safety and stimulation that being in a classroom brings," said Jean Metenier, UNICEF Deputy Representative in Haiti. "We need to get them back to learning as soon as possible. Hurricane Matthew took away their schools, homes and textbooks. It shouldn't take away their sense of hope."
According to initial national estimates, at least 300 public schools have been partially or entirely damaged in the country and many others are being used to shelter displaced families. Schools in Sud and Grande Anse departments will remain closed for at least another week.
UNICEF is working with partners to help set up temporary learning spaces and deliver school supplies. Priorities include:
Rehabilitate damaged schools;
Provide students and teachers with adequate school supplies, schools furniture and teaching materials;
Provide children with psychosocial support.
Donate now to help UNICEF ensure rapid lifesaving action for children and families affected by the storm.
About UNICEF
UNICEF is the world's leading humanitarian organization focused on children. We work in the most challenging areas to provide protection, healthcare and immunizations, education, safe water and sanitation and nutrition. As part of the United Nations, our unrivaled reach spans more than 190 countries and territories, ensuring we are on the ground to help the most disadvantaged children. While part of the UN system, UNICEF relies entirely on voluntary donations to finance our live-saving work. Please visit unicef.ca and follow us on Twitter, Facebook and Instagram.
Marie-Hélène Bachand, Communications Manager, 416 482-6552 x8425 / 514-232-4510, mbachand@unicef.ca


text:
\section{Introduction}
\label{se:intro}

In this note, we prove the following integral representation of the Bessel function of the first kind
$J_\mu(z)$, which holds for unrestricted complex values of the order $\mu$:
\beq
J_{\mu}(z) = \frac{1}{2\pi}\left(\frac{z}{2}\right)^\mu
\int_{-\pi}^\pi e^{\rmi z\cos\theta} \, \gamma^*\left(\mu,\uds\rmi z e^{\rmi\theta}\right)\rmd\theta
\qquad (\mu\in\C; z\in\C),
\label{T.0}
\eeq
where $\gamma^*$ denotes the Tricomi version of the (lower) incomplete gamma function.

Lower and upper incomplete gamma functions arise from the decomposition of the Euler integral for the
gamma function:
\begin{subequations}
\begin{align}
\gamma(\mu,w) &= \int_0^w e^{-t}\,t^{\mu-1}\,\rmd t \qquad (\Real\mu>0), \label{G.1.a} \\
\Gamma(\mu,w) &= \int_w^\infty e^{-t}\,t^{\mu-1}\,\rmd t \qquad (|\arg w|<\pi). \label{G.1.b}
\end{align}
\label{G.1}
\end{subequations}
Analytical continuation with respect to both parameters can be based either on the integrals in
\eqref{G.1} or on series expansions of $\gamma(\mu,w)$, e.g. \cite[Eq. 9.2(4)]{Erdelyi}:
\beq
\gamma(\mu,w) = \sum_{n=0}^\infty\frac{(-1)^n}{n!}\frac{w^{\mu+n}}{\mu+n},
\label{G.2}
\eeq
which shows that $\gamma(\mu,w)$ has simple poles at $\mu=0,-1,-2,\ldots$ and, in general, is
a multi-valued (when $\mu$ is not a positive integer) function with a branch point at $w=0$.
Similarly, even $\Gamma(\mu,w)$ is in general multi-valued but it is an entire function of $\mu$.
Inconveniences related to poles and multi-valuedness of $\gamma$
can be circumvented by introducing what Tricomi
called the \emph{fundamental function} of the incomplete gamma theory \cite[\S 2, p. 264]{Tricomi2}:
\beq
\gamma^*(\mu,w) = \frac{w^{-\mu}}{\Gamma(\mu)}\int_0^w e^{-t} t^{\mu-1}\,\rmd t
= \frac{e^{-w}}{\Gamma(1+\mu)}\,M(1,1+\mu;w),
\label{G.3}
\eeq
where $M(a,b;z)$ is the Kummer confluent hypergeometric function \cite[Eq. 13.2.2]{DLMF}.
The function $\gamma^*(\mu,w)$ is entire in both $w$ and $\mu$, real-valued for real $w$ and $\mu$
and $\gamma^*(-n,w)=w^n$ for $n=0,1,2,\ldots$ . B\"ohmer \cite{Bohmer}
and later Tricomi \cite{Tricomi1,Tricomi2} (see also \cite{Gautschi})
assumed $\gamma^*(\mu,w)$ as base point
for the theory, defining the incomplete gamma functions by the relations:
\begin{align}
\gamma(\mu,w) &= \Gamma(\mu) \, w^\mu \, \gamma^*(\mu,w), \label{G.4} \\
\Gamma(\mu,w) &= \Gamma(\mu) \, \left[1-w^\mu\gamma^*(\mu,w)\right]. \label{G.5}
\end{align}
For a detailed account of the incomplete gamma functions theory, see
\cite{Gautschi}, \cite[Chapter 11]{Temme} and \cite{Erdelyi,DLMF}, where massive compilations of results are stated. For what concerns details on the Bessel function, the reader is referred
to the classical treatise of Watson \cite{Watson}.

The strong link between Bessel functions and incomplete gamma functions has long been known.
Examples of this connection are represented, e.g., by the integral representations of $\gamma(\mu,w)$ in terms of $J_\mu(z)$ for $\Real\mu>0$ \cite[Eq. 9.3(4)]{Erdelyi} and of $\Gamma(\mu, w)$ in terms
of modified Bessel function of the second kind $K_\mu(z)$ for $\Real\mu<1$ \cite[Eq. 8.6.6]{DLMF}.
In this respect, it is worth mentioning also the expansions of incomplete gamma functions in
series of Bessel functions: \cite[Eqs. (2.8), (2.9)]{Gautschi}, \cite[Eqs. (40)]{Tricomi2},
and of modified Bessel functions: \cite[Eqs. 8.7.4, 8.7.5]{DLMF}, \cite[Eqs. (48), (49)]{Tricomi1}.
Formula \eqref{T.0}, whose validity extends to $(\mu,z)\in\C^2$,
makes even more explicit the intimate link between these two classes of functions.

Classical formulae of the Bessel function of the first kind $J_\mu(z)$ given by integrals
on the real line can be found in \cite[Chapter 10.9]{DLMF}, \cite[Sect. 7.3]{Erdelyi} and
\cite[Sect. 8.41]{Gradshteyn}. Many of them hold only for restricted values of $\mu$:
for instance, the classical Bessel integral \cite[p. 70]{Koronev},
\beq
J_\mu(z) = \frac{(-\rmi)^\mu}{\pi}\int_0^\pi e^{\rmi z\cos\theta}\,\cos \mu\theta\,\rmd\theta
\qquad (\mu\in\Z),
\label{T.1}
\eeq
and Poisson's integral \cite[Eq. (14.5), p. 38]{Koronev},
\beq
J_\mu(z) = \frac{1}{\Gamma(\mu+\ud)\sqrt{\pi}}\left(\frac{z}{2}\right)^\mu
\int_0^\pi e^{\rmi z\cos\theta}\,(\sin\theta)^{2\mu}\,\rmd\theta
\qquad (\Real\mu>-\uds),
\label{T.2}
\eeq
hold only for $\mu\in Z$ and $\Real\mu>-\ud$, respectively.
Additional examples are the Gubler representations \cite[Eq. 7.3(11)]{Erdelyi},
which holds for $\Real\mu<\ud$, the Mehler-Sonine integral formulae for $|\Real\mu|<\ud$
\cite[Eq. 7.12(12)]{Erdelyi} or for $|\Real\mu|<1$ \cite[Eq. 7.12(14)]{Erdelyi}.
Only the well-known Schl\"afli's and Heine's
representations hold for unrestricted complex values of the index $\mu$. Schl\"afli's
representation \cite[Eq. 7.3(9)]{Erdelyi} holds for $\mu\in\C$, with $\Real z>0$
(it holds also in case $\Real z=0$ provided that $\Real\mu>0$),
while the two Heine's expressions \cite[Eqs. 7.3(31) \& (32)]{Erdelyi} hold for $\mu\in\C$, but separately in the upper and lower half-plane of the complex $z$-plane, respectively.
In both cases, Schl\"afli's and Heine's, the representations are made up of the sum of two integrals.

Standard generalizations of Poisson's integral are obtained via its extension
to complex contour integrals, examples of which are the classical Hankel's representations
\cite[Eqs. (19.7), (19.8)]{Koronev}.
As Poisson's representation of $J_\mu(z)$ can be seen as the generalization of Bessel's integral
to complex values of $\mu$ with $\Real\mu>-\ud$ (recall that the trivial extension of formula
\eqref{T.1} to complex values of $\mu$ yields the Anger function $\mathbf{J}_\mu(z)$, instead),
mere inspection shows that formula
\eqref{T.0} can be viewed as the generalization of Poisson's integral to represent $J_\mu(z)$
at values of $\mu$ belonging to the entire complex plane, the role of $(\sin\theta)^{2\mu}$ in \eqref{T.2} being now taken by the incomplete gamma function $\gamma^*(\mu,\ud\rmi ze^{\rmi\theta})$.

The proof of formula \eqref{T.0} is given in the next section and, essentially, makes use
of elementary properties of the special functions involved. A preliminary result was given in
\cite{DeMicheli}.

\section{Integral representation for $J_\mu(z)$}
\label{se:J}

We denote by $\N_0=\{0,1,2,\ldots\}$ the set of non-negative integers.

\begin{theorem}
The following integral representation of the Bessel function of the first kind
holds true for any complex order $\mu\in\C$ and for $z\in\C$ (slit along the real negative axis when $\mu\not\in\Z$):
\beq
J_{\mu}(z) = \frac{1}{2\pi}\left(\frac{z}{2}\right)^\mu
\int_{-\pi}^\pi e^{\rmi z\cos\theta} \, \gamma^*\left(\mu,\uds\rmi z e^{\rmi\theta}\right)\rmd\theta
\qquad (\mu\in\C; z\in\C).
\label{T.00}
\eeq
\end{theorem}

\begin{proof}
Our starting point is the Gegenbauer generalization of Poisson's integral representation of the
Bessel functions of the first kind \cite[\S 3.32, Eq. (1), p. 50]{Watson}, which holds for
$\ell\in\N_0$ and $\Real\nu>-\uds$:
\beq
J_{\nu+\ell}(z) = \frac{(-\rmi)^\ell\Gamma(2\nu)\,\ell!}{\Gamma(\nu+\uds)\Gamma(\uds)\Gamma(2\nu+\ell)}
\left(\frac{z}{2}\right)^\nu\int_0^\pi e^{\rmi z\cos u}(\sin u)^{2\nu}
C_\ell^\nu(\cos u)\,\rmd u,
\label{d.J.4}
\eeq
where $C_\ell^\nu(t)$ is the Gegenbauer polynomial of order $\nu$ and degree $\ell$.
Now, we recall from \cite[Proposition 1]{DeMicheli1} the following representation of the
Gegenbauer polynomials $C_\ell^\nu(\cos u)$, which holds for $\Real\nu>0$ and $\ell\in\N_0$:
\beq
C_\ell^{\nu}(\cos u) = \frac{\Gamma(\ell+2\nu)}{2^\nu\,\ell!\,[\Gamma(\nu)]^2}
\frac{e^{-\rmi\pi\nu}}{(\sin u)^{(2\nu-1)}}
\int_u^{2\pi-u} \!\! e^{\rmi(\ell+\nu)t} \ (\cos u-\cos t)^{\nu-1}\,\rmd t \quad (u\in[0,\pi]).
\label{d.22}
\eeq
Plugging \eqref{d.22} into \eqref{d.J.4} and using the Legendre duplication formula
for the gamma function, we obtain:
\beq
J_{\nu+\ell}(z) = \frac{(-\rmi)^\ell\,e^{-\rmi\pi\nu}\, z^\nu}{2\pi\,\Gamma(\nu)}
\int_0^\pi\!\rmd u\,\sin u\,e^{\rmi z\cos u}
\int_u^{2\pi-u}\!\!e^{\rmi(\ell+\nu)\theta}\,(\cos u-\cos\theta)^{\nu-1}\,\rmd\theta.
\label{d.J.6}
\eeq
Interchanging the order of integration, \eqref{d.J.6} can be written as follows:
\beq
\begin{split}
J_{\nu+\ell}(z) &= \frac{(-\rmi)^\ell\,e^{-\rmi\pi\nu}z^\nu}{2\pi\,\Gamma(\nu)}
\left[\int_{0}^\pi\!\rmd\theta\,e^{\rmi(\ell+\nu)\theta}\int_{0}^\theta \!
e^{\rmi z\cos u} (\cos u-\cos\theta)^{\nu-1}\,\sin u\,\rmd u \right. \\
&\quad\left. +\int_\pi^{2\pi}\!\rmd\theta\,e^{\rmi(\ell+\nu)\theta}
\int_{0}^{2\pi-\theta}\!e^{\rmi z\cos u}\,(\cos u-\cos\theta)^{\nu-1}\,\sin u\,\rmd u \right].
\end{split}
\label{d.J.7}
\eeq
Next, changing the integration variables: $\theta-2\pi\to\theta$ and $u\to-u$,
the second integral on the r.h.s. of \eqref{d.J.7} becomes:
\beq
e^{\rmi\nu 2\pi}\int_{-\pi}^0 \rmd\theta \ e^{\,\rmi(\ell+\nu)\theta}
\int_0^\theta e^{\rmi z\cos u}(\cos u-\cos\theta)^{\nu-1} \sin u \,\rmd u,
\label{d.J.7.1} \nonumber
\eeq
which, inserted in \eqref{d.J.7}, yields:
\beq
\begin{split}
J_{\nu+\ell}(z) &= \frac{(-\rmi)^\ell z^\nu}{2\pi\,\Gamma(\nu)}
\left[e^{\rmi\nu\pi}\int_{-\pi}^0\!\rmd\theta\,e^{\,\rmi(\ell+\nu)\theta}
\int_{0}^\theta\!e^{\rmi z\cos u} (\cos u-\cos\theta)^{\nu-1}\sin u\,\rmd u \right. \\
&\quad\left. +e^{-\rmi\nu\pi}\int_0^{\pi}\!\rmd\theta\,e^{\rmi(\ell+\nu)\theta}\int_{0}^{\theta} \!
e^{\rmi z\cos u} (\cos u-\cos\theta)^{\nu-1}\sin u\,\rmd u \right].
\end{split}
\label{d.J.8}
\eeq
Formula \eqref{d.J.8} allows us to write $J_{\nu+\ell}(z)$ as the Fourier coefficient
of a suitable $2\pi$-periodic function, i.e.:
\beq
\rmi^\ell J_{\nu+\ell}(z) = \widetilde{\CMcal{A}}(\nu,z) \doteq
\int_{-\pi}^\pi \CMcal{A}(\theta;\nu,z) \ e^{\rmi\ell\theta}\,\rmd\theta
\qquad (\ell\in\N_0, \Real\nu>0),
\label{d.J.9}
\eeq
where $\CMcal{A}(\theta;\nu,z)$ denotes the Abel-type integral
\beq
\begin{split}
\CMcal{A}(\theta;\nu,z) &=
\frac{z^\nu}{2\pi\Gamma(\nu)}e^{\rmi\nu[\theta-\pi\sgn(\theta)]}
\int_{\cos\theta}^1 e^{\rmi zt}(t-\cos\theta)^{\nu-1}\,\rmd t \qquad (\Real\nu>0),
\end{split}
\label{d.J.10}
\eeq
and $\sgn(\cdot)$ denotes the \emph{sign function}.
Changing in \eqref{d.J.10} the integration variable $-\rmi z(t-\cos\theta)\to t$
and recalling \eqref{G.1.a}, $\CMcal{A}(\theta;\nu,z)$ can be rewritten as follows:
\beq
\CMcal{A}(\theta;\nu,z) = \frac{\rmi^\nu}{2\pi}
e^{\rmi\nu[\theta-\pi\sgn(\theta)]}e^{\rmi z\cos\theta}
\ P(\nu,-\rmi z\,(1-\cos\theta))  \qquad (\Real\nu>0),
\label{d.J.10.bis}
\eeq
where $P(\nu,w)\doteq\gamma(\nu,w)/\Gamma(\nu)$ denotes the normalised (lower) incomplete gamma function. Finally, with some algebra, we obtain from \eqref{d.J.9} and \eqref{d.J.10.bis}
the representation
\beq
J_{\ell+\nu}(z) = \frac{\rmi^{(\ell+\nu)}}{2\pi}
\int_{-\pi}^\pi e^{\rmi z\cos\theta} \, e^{-\rmi(\ell+\nu)\pi\sgn(\theta)}
\ P(\nu,-\rmi z\,(1-\cos\theta)) \ e^{\rmi(\ell+\nu)\theta}\,\rmd\theta,
\label{f.3}
\eeq
which holds for $\ell\in\N_0$ and $\Real\nu>0$.
Now, we want to show that the integral in \eqref{f.3} does not change if we substitute the factor
$P(\nu,-\rmi z\,(1-\cos\theta))$ with
$P(\ell+\nu,-\rmi z\,(1-\cos\theta))$. To this end, we recall that $P(\nu,w)$ satisfies
the following recurrence relation \cite[Eq. 8.8.11]{DLMF}:
\beq
P(\ell+\nu,w)=P(\nu,w)-w^\nu\,e^{-w}\sum_{k=0}^{\ell-1}\frac{w^k}{\Gamma(\nu+k+1)}
\qquad (\ell\geqslant 0),
\label{f.3.1}
\eeq
the sum being obviously understood to be null when $\ell=0$.
We have:
\beq
\begin{split}
&\int_{-\pi}^\pi e^{\rmi z\cos\theta} \, e^{-\rmi(\ell+\nu)\pi\sgn(\theta)}
\ P(\ell+\nu,-\rmi z\,(1-\cos\theta)) \ e^{\rmi(\ell+\nu)\theta}\,\rmd\theta \\
&=\int_{-\pi}^\pi e^{\rmi z\cos\theta} \, e^{-\rmi(\ell+\nu)\pi\sgn(\theta)}
\ P(\nu,-\rmi z\,(1-\cos\theta)) \ e^{\rmi(\ell+\nu)\theta}\,\rmd\theta \\
&\quad-(-\rmi z)^\nu e^{\rmi z} \sum_{k=0}^{\ell-1}\frac{(-\rmi z)^k}{\Gamma(\nu+k+1)}
\int_{-\pi}^\pi e^{-\rmi(\ell+\nu)\pi\sgn(\theta)}(1-\cos\theta)^{\nu+k}e^{\rmi(\ell+\nu)\theta}
\,\rmd\theta.
\end{split}
\label{f.3.2}
\eeq
By using formula \cite[Formula 3.63.9]{Gradshteyn}, the rightmost integrals on the r.h.s.
of \eqref{f.3.2} can be readily computed:
\beq
\begin{split}
&\int_{-\pi}^\pi e^{-\rmi(\ell+\nu)\pi\sgn(\theta)}(1-\cos\theta)^{\nu+k}e^{\rmi(\ell+\nu)\theta}
\,\rmd\theta
= 2^{\nu+k+2} \int_{0}^{\pi/2} (\cos\theta)^{2(\nu+k)}\,\cos[2(\ell+\nu)\theta]\,\rmd\theta \\
&=\frac{2^{1-\nu-k}\pi}{(2\nu+2k+1) \ B(2\nu+k+\ell+1,k-\ell+1)},
\label{f.3.3}
\end{split}
\eeq
where $B(\cdot,\cdot)$ denotes the Euler beta function. For $\Real\nu>-\ud$ and $\ell\geqslant 0$,
the integrals in \eqref{f.3.3} are therefore null for $0\leqslant k\leqslant \ell-1$.
Hence, in view of this latter result, we now set $\mu=\ell+\nu$, and from \eqref{f.3} we have:
\beq
J_{\mu}(z) = \frac{\rmi^{\mu}}{2\pi}
\int_{-\pi}^\pi e^{\rmi z\cos\theta} \, e^{-\rmi\mu\pi\sgn(\theta)}
\ P(\mu,-\rmi z\,(1-\cos\theta)) \ e^{\rmi\mu\theta}\,\rmd\theta
\qquad (\Real\mu>0).
\label{f.3.4}
\eeq
Now, we change the integration variable $\theta-\pi\sgn(\theta) \to \theta$, write
$(1+\cos\theta) = \ud e^{-\rmi\theta}(1+e^{\rmi\theta})^2$ and, in view of the
$2\pi$-periodicity of the integrand, formula \eqref{f.3.4} becomes:
\beq
J_{\mu}(z) = \frac{\rmi^{\mu}}{2\pi}
\int_{-\pi}^\pi e^{-\rmi z\cos\theta} \, P(\mu,-\uds\rmi z e^{-\rmi\theta}(1+e^{\rmi\theta})^2)
\, e^{\rmi\mu\theta}\,\rmd\theta \qquad (\Real\mu>0).
\label{f.4}
\eeq
Note that $P(\mu,w)$ is an entire function of $\mu$ but it is a multi-valued function of $w$
with a branch point at $w=0$.

\vspace{0.2cm}

Consider for $\lambda\in[0,\infty)$ the integral
\beq
S_{z,\mu}(\lambda)\doteq
\int_{-\pi}^\pi s_{z,\mu}(\theta,\lambda) \,\rmd\theta \qquad (\Real\mu>0,z\in\C; \lambda\in[0,+\infty)),
\label{d.1}
\eeq
where
\beq
s_{z,\mu}(\theta,\lambda) \doteq e^{-\rmi z\cos\theta} \, P(\mu,g_\theta(\lambda))
\, e^{\rmi\mu\theta} \qquad (\theta\in(-\pi,\pi), \lambda\in[0,+\infty);\Real\mu>0),
\label{d.1.1}
\eeq
with $g_\theta(\lambda)=-\uds\rmi z e^{-\rmi\theta}(1+e^{\rmi\theta})^\lambda$.
Evidently, $2\pi\,J_\mu(z)=\rmi^\mu S_{z,\mu}(2)$.
The function $S_{z,\mu}(\lambda)$ is actually independent of $\lambda$ for $\lambda\geqslant0$
and $\Real\mu>0$. To see this, we analyze the derivative with respect to $\lambda$,
$\partial_\lambda S_{\mu,z}(\lambda)$.
The function $s_{z,\mu}(\theta,\lambda)$ is continuous in
$(\theta,\lambda) \in (-\pi,\pi) \times [0,\infty)$ with
\beq
\int_{-\pi}^\pi \left|s_{z,\mu}(\theta,\lambda)\right|\,\rmd\theta
\leqslant
c_1(\mu,z) \, \exp\left[2^{\lambda-1}|z|+(\lambda-1)|\mu|\right] < \infty \qquad (\Real\mu>0),
\label{d.2.1}
\eeq
for finite values of $\lambda$, $c_1(\mu,z)$ being a finite constant indipendent of $\lambda$.
Similarly, recalling that $\partial_w P(\mu,w) = w^{\mu-1}\,e^{-w}/\Gamma(\mu)$ \cite[Eq. 8.8.13]{DLMF}, we have
\beq
\partial_\lambda s_{z,\mu}(\theta,\lambda)
= \frac{e^{-\rmi z\cos\theta}}{\Gamma(\mu)}\,[g_\theta(\lambda)]^\mu\,e^{-g_\theta(\lambda)}\,\ln(1+e^{\rmi\theta})\,e^{\rmi\mu\theta},
\label{d.2.2}
\eeq
which is continuous in $(\theta,\lambda) \in (-\pi,\pi) \times [0,\infty)$ with:
\beq
\int_{-\pi}^\pi \left|\partial_\lambda s_{z,\mu}(\theta,\lambda)\right|\,\rmd\theta
\leqslant
c_2(\mu,z) \, \exp[2^{\lambda-1}|z|+(\lambda-1)|\mu|]\int_{-\pi}^\pi\left|\ln(1+e^{\rmi\theta})\right|\,\rmd\theta < \infty
\label{d.2.3}
\eeq
for finite values of $\lambda$, $c_2(\mu,z)$ being a finite constant indipendent of $\lambda$.
Hence, differentiation under the integral sign is legitimate and we have:
$\partial_\lambda S_{z,\mu}(\lambda)= \int_{-\pi}^\pi\partial_\lambda s_{z,\mu}(\theta,\lambda)\,\rmd\theta$ for $\lambda\geqslant 0$.

Let us introduce the complex variable $w=1+e^{\rmi\theta}$ and, for $\Real\mu>0$ and
$\lambda\geqslant 0$, the function
\beq
f_{z,\mu,\lambda}(w) \doteq \frac{1}{\Gamma(\mu)}\left(-\frac{\rmi z}{2}\right)^\mu
\exp\left(-\frac{\rmi z}{2}\frac{w^2-w^\lambda-2w+2}{w-1}\right)
w^{\lambda\mu}\,\ln w \qquad (\Real\mu>0,\lambda\geqslant 0).
\label{d.6}
\eeq
We have:
\beq
\partial_\lambda S_{\mu,z}(\lambda)=
\oint_{C(1,1)} f_{z,\mu,\lambda}(w) \, \rmd w,
\label{d.7}
\eeq
where $C(1,1)$ denotes the circle with center $w=1$ and radius $R=1$.
The points of $f_{z,\mu,\lambda}(w)$ which require attention are $w=0$ and $w=1$.
We have (recall that $\Real\mu>0$):
\beq
\lim_{w\to 0} f_{z,\mu,\lambda}(w) = \left(-\frac{\rmi z}{2}\right)^\mu \frac{e^{\rmi z}}{\Gamma(\mu)}
\lim_{w\to 0} w^{\lambda\mu}\ln w = 0 \quad\mathrm{for}\quad\lambda>0.
\label{d.8}
\eeq
Moreover, $\lim_{\lambda\to 0^+}\lim_{w\to 0} f_{z,\mu,\lambda}(w) = 0$,
the two limits being evidently not interchageable.
For what concerns the point $w=1$, we have:
\beq
\lim_{w\to 1} f_{z,\mu,\lambda}(w) = \frac{1}{\Gamma(\mu)}
\left(-\frac{\rmi z}{2}\right)^\mu e^{\rmi \lambda z/2} \lim_{w\to 1} \ln w = 0
\quad\mathrm{for}\quad\lambda\in[0,\infty).
\label{d.10}
\eeq
Hence, for any $\lambda>0$, $f_{z,\mu,\lambda}(w)$ is a single-valued holomorphic function
with no singularities on and within the circle $C(1,1)$. Then, by Cauchy theorem the integral in
\eqref{d.7} vanishes and $\partial_\lambda S_{\mu,z}(\lambda) = 0$ for $\lambda>0$.
Moreover, from \eqref{d.2.2} we have for $\lambda=0$:
\beq
\left.\partial_\lambda S_{\mu,z}(\lambda)\right|_{\lambda=0}
=\frac{1}{\Gamma(\mu)}\left(-\frac{\rmi z}{2}\right)
\int_{-\pi}^\pi \exp\left[-\rmi z e^{\rmi\theta}/2\right]\ln(1+e^{\rmi\theta})\,\rmd\theta=0
\label{d.10.1}
\eeq
For the continuity of $\partial_\lambda S_{\mu,z}(\lambda)$ for $\lambda\geqslant 0$ which follows
from \eqref{d.2.2} and \eqref{d.2.3}, $\partial_\lambda S_{\mu,z}(\lambda) = 0$
for $\lambda\geqslant 0$ and $\Real\mu>0$.
Consequently, from \eqref{f.4} we can write:
\beq
J_{\mu}(z) = \frac{\rmi^{\mu}}{2\pi}
\int_{-\pi}^\pi e^{-\rmi z\cos\theta} \, P(\mu,-\uds\rmi z e^{-\rmi\theta})\,e^{\rmi\mu\theta}\,\rmd\theta
\qquad (\Real\mu>0).
\label{f.5}
\eeq
Since $P(\mu,w)=w^\mu\,\gamma^*(\mu,w)$ (see \eqref{G.4}),
\eqref{f.5} yields:
\beq
J_{\mu}(z) = \frac{1}{2\pi}\left(\frac{z}{2}\right)^\mu
\int_{-\pi}^\pi e^{-\rmi z\cos\theta} \, \gamma^*(\mu,-\uds\rmi z e^{-\rmi\theta})\,\rmd\theta
\qquad (\Real\mu>0),
\label{f.6}
\eeq
which, simply changing the integration variable $\theta\to\pi-\theta$ and by the
$2\pi$-periodicity of the integrand, finally gives formula \eqref{T.0}.
The restriction $\Real\mu>0$ is immaterial since both parts of the equality \eqref{f.6}
are analytic functions of $\mu$ (recall that $\gamma^*(\mu,w)$ is entire in $\mu$ and $w$)
and, according to the principle of analytic continuation, the result is valid for any $\mu\in\C$
and $z\in\C$ (this latter domain being slit along the real negative axis when $\mu$ is not integer).
\end{proof}

It is obvious that, by a trivial change of variable, formula \eqref{T.0} can be rewritten in terms of
the generating function for the Bessel functions of the first kind of integral order:
\beq
e^{\rmi z\sin\theta} = \sum_{n=-\infty}^\infty J_n(z) \, e^{\rmi nz}.
\label{Generating}
\eeq
We have:
\beq
J_\mu(z) = \frac{1}{2\pi}\left(\frac{z}{2}\right)^\mu \int_{-\pi}^\pi
e^{\rmi z\sin\theta}\,\gamma^*\left(\mu,\uds z e^{\rmi\theta}\right)\,\rmd\theta
\qquad (\mu\in\C,z\in\C).
\label{Generating.1}
\eeq
Formula \eqref{T.0} can be extended in following way. First, recall the following recurrence
relation for $\gamma^*(\mu,w)$, which follows from \eqref{f.3.1} and \eqref{G.4}:
\beq
\gamma^*(\mu+n,w)
=w^{-n}\left(\gamma^*(\mu,w)-e^{-w}\sum_{k=0}^{n-1}\frac{w^k}{\Gamma(\mu+k+1)}\right)
\qquad (n\geqslant 0).
\label{f.7}
\eeq
Then we consider $J_{\mu+n}(z)$ with $n\geqslant 0$. From \eqref{T.0} and \eqref{f.7} we have:
\beq
\begin{split}
J_{\mu+n}(z) &= \frac{1}{2\pi}\left(\frac{z}{2}\right)^\mu
\int_{-\pi}^\pi e^{\rmi z\sin\theta} \, \gamma^*\left(\mu,\uds z e^{\rmi\theta}\right)
e^{-\rmi n\theta}\,\rmd\theta \\
& \quad-\sum_{k=0}^{n-1}\frac{(z/2)^{\mu+k}}{\Gamma(\mu+k+1)}
\int_{-\pi}^\pi \exp(-\uds ze^{-\rmi\theta}) e^{\rmi(k-n)\theta}\,\rmd\theta
\quad (n\geqslant 0).
\end{split}
\label{f.8}
\eeq
Now, it is easy to show that the rightmost integrals on the r.h.s. of \eqref{f.8} are
null for $k \leqslant n-1$. Therefore, we have:
\beq
J_{\mu+n}(z) = \frac{1}{2\pi}\left(\frac{z}{2}\right)^\mu
\int_{-\pi}^\pi e^{\rmi z\sin\theta} \, \gamma^*(\mu,\uds z e^{\rmi\theta})
e^{-\rmi n\theta}\,\rmd\theta \qquad (n\geqslant 0;\mu\in\C,z\in\C),
\label{f.9}
\eeq
that is, for $n\geqslant0$, $2\pi(z/2)^{-\mu}J_{\mu+n}(z)$ coincides with the
Fourier coefficient $\widetilde{\kappa}_{-n}(\mu,z)$ (see \eqref{d.J.9}) of the function
$\kappa(\theta;\mu,z)\doteq e^{\rmi z\sin\theta} \, \gamma^*(\mu,\uds z e^{\rmi\theta})$.
Representation \eqref{Generating.1} can thus be viewed as the particular case
with $n=0$ of formula \eqref{f.9}.  Analogously, the Fourier coefficients
$\widetilde{\kappa}_{n}(\mu,z)$ for $n>0$ are easily proved to be
\beq
\widetilde{\kappa}_{n}(\mu,z)
= 2\pi\left(\frac{z}{2}\right)^{-\mu}\sum_{k=n}^\infty\frac{(-1)^k}{k!}\frac{1}{\Gamma(\mu-n+k+1)}
\left(\frac{z}{2}\right)^{2k+\mu-n} \quad (n > 0),
\label{fourier.1}
\eeq
the sum on the r.h.s. of \eqref{fourier.1} being the \emph{shifted}
(i.e., starting from $k=n$) power series defining $J_{\mu-n}(z)$ (see \cite[Eq. 10.2.2]{DLMF}).

\vspace{0.5cm}

The structure of formula \eqref{T.0} (and \eqref{Generating.1}) yields readily analogous
companion results for functions related to the Bessel function of the first kind.
To exemplify, a couple of instances are given below.

\begin{proposition}
\label{pro:1}
The modified Bessel function of the first kind $I_\mu(z)$ has the following integral representation
for unrestricted complex values of $\mu$ and $z$:
\beq
I_\mu(z) = \frac{1}{2\pi}\left(\frac{z}{2}\right)^{\mu}
\int_{-\pi}^\pi e^{z\cos\theta}\,\gamma^*(\mu,\uds z e^{\rmi\theta})\,\rmd\theta
\qquad (\mu\in\C; -\pi\leqslant\arg z<\pi).
\label{T.4}
\eeq
\end{proposition}
\begin{proof}
Formula \eqref{T.4} follows from the connection relation \cite[Eq. 10.27.6]{DLMF}:
\beq
I_\mu(z) = e^{\mp\rmi\mu\pi/2}J_\mu(z e^{\pm\rmi\pi/2})
\qquad \left(-\pi\leqslant\pm\arg z\leqslant{\frac{\pi}{2}}\right).
\label{T.3}
\eeq
\end{proof}
As an additional example, from formula \eqref{Generating.1}, an analogous new integral representation for the derivatives of $J_\mu(z)$
follows.

\begin{proposition}
\label{pro:2}
For any $\mu,z\in\C$, the $k$th derivative with respect to $z$ of the Bessel function of
the first kind, $\partial^k_z J_\mu(z)$, ($k\in\N_0$), can be represented by the following integral:
\beq
\partial_z^k J_\mu(z)
= \frac{1}{2\pi}\left(\frac{z}{2}\right)^{\mu-k}
\int_{-\pi}^\pi e^{\rmi z\sin\theta}\,\gamma^*(\mu-k,\uds z e^{\rmi\theta})(\rmi\sin\theta)^k
\,e^{-\rmi k\theta}\,\rmd\theta \quad (k\in\N_0).
\label{T.10}
\eeq
\end{proposition}

\begin{proof}
Representation \eqref{T.10} follows immediately by plugging \eqref{Generating.1} into the
following formula for the derivative of the Bessel function of the first kind \cite[Eq. 10.6.7]{DLMF}:
\beq
\partial_z^k J_\mu(z) = 2^{-k}\sum_{m=0}^k (-1)^m\binom{k}{m}\,J_{\mu-k+2m}(z),
\label{T.11}
\eeq
and recalling that $\sum_{m=0}^k (-1)^m\binom{k}{m}\exp(-2\rmi m\theta)=(1-\exp(-2\rmi\theta))^k$.
\end{proof}

Formula \eqref{T.10} can be analytically continued to $k\in\C$ with $\Real k >-1$, thus yielding an integral representation for the fractional derivative of the Bessel function of the first kind.

\begin{note}
\rm
In view of relation \eqref{G.3} between the Tricomi incomplete gamma function $\gamma^*$ and the Kummer confluent hypergeometric function $M$, the main results of this work can be formulated
also in terms of the latter. Therefore, the integral representation of the Bessel function of the first
kind \eqref{T.00} reads:
\beq
J_{\mu}(z) = \frac{1}{2\pi}\frac{(z/2)^\mu}{\Gamma(1+\mu)}
\int_{-\pi}^\pi e^{\ud\rmi z \, e^{-\rmi\theta}} \, M\left(1,1+\mu,\uds\rmi z e^{\rmi\theta}\right)\rmd\theta
\qquad (\mu\in\C; z\in\C).
\label{T.12}
\eeq
The modified Bessel function of the first order $I_\mu(z)$ reads (see \eqref{T.4}):
\beq
I_\mu(z) = \frac{1}{2\pi}\frac{(z/2)^\mu}{\Gamma(1+\mu)}
\int_{-\pi}^\pi e^{\ud z \, e^{-\rmi\theta}} \,M\left(1,1+\mu;\uds z e^{\rmi\theta}\right)\,\rmd\theta
\qquad (\mu\in\C; -\pi\leqslant\arg z<\pi),
\label{T.13}
\eeq
while the integral representation of the $z$-derivative of fractional order $k$, with $k\in\C$ and $\Real k >-1$, of the Bessel function of the first kind, $\partial_z^k J_\mu(z)$, can be written as
(see\eqref{T.10}):
\beq
\partial_z^k J_\mu(z)
= \frac{1}{2\pi}\frac{(z/2)^{\mu-k}}{\Gamma(1+\mu-k)}
\int_{-\pi}^\pi e^{-\ud z\, e^{-\rmi\theta}}\,M\left(1,1+\mu-k,\uds z e^{\rmi\theta}\right)(\rmi\sin\theta)^k
\,e^{-\rmi k\theta}\,\rmd\theta,
\label{T.14}
\eeq
where the principal branch of the power is taken when $k$ is a non-integer number.
\end{note}

\bibliographystyle{amsplain}

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text:
Tupou al VI-lea (ʻAhoʻeitu ʻUnuakiʻotonga Tukuʻaho Tupou VI; n. 12 iulie 1959) este rege al Tonga. Este fratele mai mic al ultimului rege George Tupou al V-lea. A fost oficial confirmat de fratele său la 27 septembrie 2006 ca moștenitor prezumptiv al tronului deoarece regele nu avea copii legitimi.

Biografie
S-a născut ca al treilea fiu și cel mai mic copil al regelui Tāufaāhau Tupou al IV-lea. A fost educat la Cambridge în perioada 1973-1977. Și-a început cariera militară alăturându-se marinei în 1982; a devenit locotenet comandant în 1987.

În 1998 și-a încheiat cariera militară pentru a face parte din guvern, inițial ca ministru al apărării și ca ministru de externe în același timp din octombrie 1998 până în august 2004. A preluat aceste posturi de la fratele său mai mare Tupoutoʻa, la acel moment prinț moștenitor al tronului. Curând, la 3 ianuarie 2000, a fost numit prim ministru, funcție pe care a deținut-o până la brusca sa demisie la 11 februarie 2006, pentru un motiv care nu a fost clar, dar probabil a fost din cauza tulburărilor din țară de la mijlocul anului 2005; o serie de proteste pro-democrație au cerut un rol mai mic al familiei regale în guvernare.

În 2008 Ahoeitu a fost numit primul Înalt Comisionar pentru Australia, post pe care l-a deținut până la ascensiunea sa pe tronul tongalez în 2012.

Arbore genealogic

Note

Nașteri în 1959
Monarhi actuali
Lideri naționali actuali
Prim-miniștri ai Tongăi
Monarhi tongalezi

redpajama_set_name: RedPajamaWikipedia


text:
Open House doors swing open
By WI Reporters on November 1, 2014 • ( Leave a comment )
CHARLOTTE BINNING, DIANA ZAMIR, AARON BRYANS
Architecture and design are on show this weekend as part of the third annual Open House Perth drawing attention to the city's modern spectacles and hidden treasures.
More than 70 destinations are on show this year, including public buildings and houses spread over Perth's CBD and inner suburbs.
In Mount Hawthorn, ANZAC Cottage, built in 1926, was open to the public.
The cottage was built in one day by the Mt Hawthorn community as a home for Anne Chapple's grandfather, Private Cuthbert Porter who was one of the first soldiers to land in Gallipoli.
Mrs Chapple said ANZAC Cottage was a very important part of her family history.
Mrs Porter with Mrs Chapple in the room in which Mrs Porter was born.
"It's home for us," she said, even though the family has not lived there since the early 1980s.
"It's a remembrance from my grandparents and my mum has strong memories of living here.
"My mother was born in this house and she lived here until she was 21."
Mrs Chapple said the cottage – which was Australia's first memorial to the Great War – is still a symbol of the respect and regard people have for Australia's servicemen and women.
"I open the cottage every month because it's wonderful hearing other people's stories," she said.
"The Cottage is a place where people can come to remember and be thankful."
Marjorie Porter was born in ANZAC Cottage on January 3, 1921 and has very fond memories of the house.
"I used to get a little bit indignant about people walking on the footpath and reading the marble plaque outside," she said.
Mrs Porter said the cottage was a very important part of growing up.
"It's the history of so many people trying to do the right thing, trying to protect their shores and fighting for their country."
Over in the heart of Perth's Cultural Centre, the Art Gallery of Western Australia is a popular location for the annual Open House.
"I think it's nice to open houses up that are usually closed to the public, and let them see what's going on inside the building," tour guide Timo Bleeker said.
Art gallery tour guides Timo Bleeker and Nelly Kohar
With a design inspired by the Mexican Museum of Anthropology, the gallery's main building is modernist in style and was designed by architect Charles Sierakowski.
"It's great that we can see what the architecture is like and to promote architecture to the public," Mr Bleeker said.
Museum-goer Rebecca Wallace from Manjimup visited the art gallery with her daughters while the three were in town.
"I love all the different things about the art gallery," Ms Wallace said.
Mr Bleeker said he first volunteered for Open House last year.
"Even more buildings are participating this year, so we believe there will be an even larger crowd," he said.
DESIGNING THEIR WAY TO SUCCESS
Alongside bigger buildings such as Parliament House and the Telstra Exchange, smaller studios have opened their doors to highlight work within.
King Street Studio co-owners Nic Brunsdon and Jordy Hewitt
King Street Studio co-owner Jordy Hewitt said Open House was an exciting opportunity for designers looking to showcase their work.
"It's great, King Street was in it last year as well," she said.
"It's good to get people involved in art and design and architecture.
"We've been promoting it and it's been a good excuse to have round two of putting my work up."
The studio itself is split into two sections, Hewitt's stairs gallery and her partner Nic Brunsdon's Post-Studio which works with Spacemarket to re-create unused spaces.
"We launched the stairs gallery at the end of August," Hewitt said.
"I had 32 pieces and we had a kind of opening party and either they've sold or gone to other events."
PICA JOINS THE SHOW
The rich history of the Perth Institute of Contemporary Art was also open for viewing, joining the list of active destinations for its first year of Open House.
Gallery attendant, Tim Green
Front of house manager Amy Perejuan-Capone says the building had been used as an education facility up until 1988.
"It was built as a central Perth school and became the Perth Boys School in 1947, after that becoming a high school and technical college before becoming an art gallery in 1988," Ms Perejuan-Capone said.
She said Open House was a good idea for people to get to know the city, and the mix of contemporary and heritage-listed buildings was interesting.
PICA showcases contemporary art through different mediums such as exhibitions, dance, theatre and live art projects.
It also provides workshops and classes for up-and-coming local artists.
Gallery attendant Tim Green said Open House was a "really great initiative".
"It's really great for people to see the skeletons of these really amazing old heritage buildings that we have so few of in Perth," Mr Green said.
Categories: News Day, Property
Tagged as: Open House
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Toki pona (betyder bra, eller enkelt, språk på toki pona) är ett minimalistiskt konstruerat språk skapat 2001 av den kanadensiska översättaren och lingvisten Sonja Lang. Grundtankarna med toki pona är inspirerade av daoistisk filosofi, och det som värderas högst i språket är enkelhet och godhet (som båda heter pona på toki pona).

Tanken är att mycket som vi mår dåligt av och som är negativt med dagens västerländska livsstil är orsakat att vi gör saker och ting för komplexa och abstrakta. Toki pona är konstruerat för att man ska fokusera på grundläggande och viktiga saker när man talar (premissen är att språket man använder påverkar ens sätt att tänka), vilket får det att likna ett pidginspråk..

Ordförrådet är därför litet, ursprungligen endast 120 ord uppbyggda av 14 möjliga ljudenheter, men konstruerat att varje ord representerar begrepp på ett högt abstraktionsplan. Det betyder alltså att ett ord kan ha flera betydelser som är associerade med varandra, och vars tolkning därför i allra högsta grad blir kontextberoende, beroende av sammanhanget ordet står i. Till exempel ordet toki betyder bland annat "att tala", "att säga", "att tänka", "att kommunicera" och "att använda språket". Ordet ilo betyder bland annat "verktyg", "maskin" och "apparat". Tillsamman blir de "telefon", ilo toki.. I praktiken är det sällan man behöver specificera så tydligt vad man menar i ett vardagligt samtal, och det är just enkelheten som är tanken med toki pona.

Det finns ungefär 100 personer som kan flytande toki pona.

Källor

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 Sapir-Whorf-hypotesen
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Externa länkar
 Toki ponas officiella hemsida
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Konstgjorda språk


Siân Halcrow has research interests in Southeast Asian prehistory, as well as infant and child health and disease in the past.
As archaeologists, we not only work with the dead but also often with living cultures different from our own, writes Siân Halcrow.
That's the type of comment I often receive when I describe my work to people.
While archaeologists do use many methods in common with forensics, the aims of our research are very different, and the relationships with the people we study are also different and wrapped up with much complexity.
I carry out my research in different parts of Southeast Asia: Thailand, Cambodia, Laos, Vietnam and Indonesia. I focus on understanding the impacts of the intensification of agriculture on humans, and the roots of Asian civilisations, through the most direct means: The human skeleton.
Southeast Asia is less well known archaeologically than East Asia and the "West", but it is an important place to analyse human adaptation and disease evolution in its unique, varied biological and social environments.
The research in Southeast Asia is especially important as archaeological models based on subsistence change in the Americas, Europe or Near East are likely not relevant worldwide.
Some recent projects I'm working on include the Plain of Jars sites in Laos, which are pending Unesco World Heritage status. I also manage the skeletal collection from a late Iron Age site in northeast Thailand, called Non Ban Jak. This work is especially important, in terms of looking at the development of social complexity directly prior to the development of the Kingdom of Angkor that extended its control into this region.
We work on painstaking excavating sites, recording burials in situ, and then dry, pack, transport, clean, and analyse the skeletons with the ultimate aim to disseminate this knowledge through papers and talks.
As archaeologists, we are not only working with the dead but also often working with living cultures different from our own.
What's not often investigated in our field is the way we feel about, and relate to, the people we work with – both the dead and the living.
Ethics are an important component of investigating cultural attitudes to death. But what is ethical is largely dependent on the social and cultural context.
The ethics of dealing with the dead are particularly complex for foreign archaeologists like myself working in Southeast Asia.
Southeast Asia has a long and often brutal colonial history, and archaeology was a favoured tool of the colonisers. Southeast Asians today are now becoming more conscious of maintaining their independence, including in research.
Over the past few decades, there has been a movement for local management of projects and genuine collaboration between foreigners and locals. Alongside this, there has been repatriation of human remains from many international museums back to local communities.
Many archaeologists working in Thailand are now dedicated to building local expertise through research and training. However, there is still a power differential in who holds the funding for excavation and specialty research facilities.
As a New Zealander working in Asian archaeology, my belief system is often at odds with the people that we are working with in the past and present. My work with human skeletal remains from archaeological sites in Northeast Thailand is very much accepted by the Thai in large part due to Buddhism, where the body is seen more like a vessel.
But differences in beliefs were significant in my work with indigenous groups in the Cambodian Cardamom Mountains. The ancient people from these sites were likely animists. The practice of exhuming the dead would have been abhorrent to them. Our practice had to comply with the community beliefs of their relationship with the dead. All skeletal remains apart from small samples had to be reburied immediately after analyses.
A recent experience in Thailand really brought home to me the difference in how I interact with the long dead and the recent dead.
One day, our next-door neighbour came to our house where we were doing our analyses. She seemed interested in my work and asked if I could help her identify which bones were which. While I was bemused at why she would want to know this, I agreed.
She then invited me to her house and presented me with a large basket with the cremated remains of her late husband. She wanted me to identify the uncrushed fragments!
I often feel a disconnect with people from the past. Maybe this is some kind of coping mechanism, similar to what is often described by forensic anthropologists when dealing with the recently deceased. But looking at the cremated remains of the woman's husband was very difficult for me emotionally.
Archaeological practice can be more than just analyses of scientific finds.
It is an untapped opportunity to look at cross-cultural understandings of relationships between the living and the dead, and therefore, the inner workings of our societies.
Views expressed in this article are personal to the author.


The term blog is short for web log. It is a web page where you can log in regularly and post text or graphics content. There are blogs that you can have for free while others you would have to pay for. Sites like WordPress, Blogger, and MyBlogSite offer free blog space. Because of this, a blog is probably the most convenient way to own a personal site online. Blogs can be personal, professional, or business. Personal blogs are purely personal journals of their owner. Pro blogs or professional blogs are created to earn income by posting ads and writing articles to promote certain products or services for a fee. Meanwhile, business blogs are created for the purpose of promoting the products or services sold by the blog owner. Blogging for business has become the new trend among businessmen today.
A blog is more convenient to use than a regular website. Other than its cost efficiency, it is also easier to manage. You can easily make all its content appear in the main page, unlike with websites where you may have to deal with different pages. Your posts can contain texts, photos, graphics, and videos. Entries appear chronologically, usually with the latest occupying the topmost area. Plus, blogs can also be easily updated.
A blog archive is a collection of old posts which are usually grouped by week or month. The archive is usually located in the blog's sidebar or near the header, somewhere that will facilitate easy access to old posts.
Related blog entries can be grouped into categories such as products, promos, services, and others. This will facilitate easy access of visitors to those entries that catch their interest.
This is a list of blogs that you like or follow, located in your blog's sidebar or below for easy access. You can include your other blog sites in your blogroll so that your blog viewers can link to them easily. If your business is flower arrangements and you're also selling gardening supplies, for example, you can place a link to your gardening supplies blog in the blogroll of your flower arrangement page. Blogrolls are great traffic generator. If you are included in the blogroll of other sites and blogs, your site will get a greater exposure. Site visitor can easily click on your link and arrive on your site. And if your blog has many incoming links from other high quality blogs, it will rank higher in search engines.
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She wanted healthy balance in her family's life — and in their investment portfolio. That's why Juice It Up! entered the picture.
As owners of three Wienerschnitzel franchises, Sylvia Quirino and her husband, John Davis, were already experienced franchise owners when they were introduced to Juice It Up! They already had an in-depth understanding of the ins and outs of a food franchise. And as much as they love their experience with the fast-food franchise, they felt a certain balance was missing. So they started looking for a healthy food franchise to invest in. Read about their experience in this Juice It Up! franchise review.
What was it that made you want to find either a juicing franchise or Juice It Up! specifically?
I wanted a healthier lifestyle, because I would just eat out and not too healthy. My concern was for myself and my family to start eating more healthy, being more healthy, having a better lifestyle.
When you started exploring the healthy food franchise segment, what was that journey like? What brought you to Juice It Up? What caught your attention?
We liked just going in there, and it seemed fresh and it smelled good. That's what made us go in. We loved Juice It Up! so we would go and get smoothies, but we didn't know that they had juices and bowls, so that attracted us when we started going in. There was so much more variety than just smoothies.
You and your husband opened your first unit in 2017 in Rialto. What are your plans in terms of expansion?
We are there. If there's any opportunity to do it, we would love to do it.
When you started looking at Juice It Up!, you were customers first. Did you take a look at other juice franchises or other smoothie franchises?
We did. We went more for Juice It Up! because when we went to the other places, we just didn't like them as much. We didn't like the names. Also, we really liked Juice It Up! as a customer, so we wanted to get something that we loved as customers.
There are so many juice places out there. How does Juice It Up! set itself apart from the competition?
For us, I like the name. The name stands out for me and also the juice bar. It gives the customers a healthier juice, made fresh to order from high quality ingredients, so it's not just the smoothies but the juice part of it. I wanted to have more of the green part of drinking, like kale and spinach and all of those things being put into a juice. That's what I liked.
The menu variety at Juice It Up! was a big factor in Sylvia Quirino's decision to invest.
How are you staffing your Juice It Up?
I am an owner-operator. I come in and do prep for the day, take orders, stock. I help my employees train. If I get a new employee, I train them. I usually have eight or nine people, with two full-time managers.
You were obviously sold as a consumer, but when you started looking at this as an investor, what were your thoughts about the direction the brand is headed in?
I love it because the way they're going is they want to expand, and also they want to emphasize more of the bowls and juices, which increases the check average. I like the fact that they're going in the right direction.
You said that you really wanted to find healthier options for yourself and your family. Can you tell me a little bit about your family?
One thing that attracted me to Juice It Up! is that my kids do not like vegetables, so I wanted something that would make them take them. I'll put kale and spinach in my 7-year-old's smoothie. He'll taste a little bit, but that way he's still getting his little vegetables in there. My 11-year-old son loves smoothies, so I try also to put as many vegetables as I can in there, but he's a little bit older so he knows what I'm doing. I also have a 14-year-old girl, and our 21-year-old daughter is one of my managers.
So he's onto you, but he's willing to give it a try because it tastes so good.
What are your long-term goals for your Juice It Up! business?
What we're hoping to do is just pass it to our kids, if any of them wants to take over. We would love that.
Knowing what you know now, after a year of being in business, if you were just starting out again, would you still become a Juice It Up! franchisee?
Yes, I would. I love it. I love what I'm doing. I love adjusting to our customers. I love the product. If I had to do it again, I definitely would do it again.
If you think you've got what it takes to make a great Juice It Up! franchisee, we'd love to have a conversation. Just fill out the form on this page. We'll send you a password for our proprietary Juice It Up! Franchise Information Center, where you read more Juice It Up! franchise reviews and review in-depth data our company. Meanwhile, we invite you to continue exploring our detailed research pages.


2019-02-02T19:20:03-05:00https://images.c-span.org/Files/594/20190202193333002_hd.jpgFormer intelligence officer David Priess provided a history of the ways in which presidents have been removed from office. Larry Pfeiffer introduced Mr. Priess and moderator Susan Glasser.
Former intelligence officer David Priess provided a history of the ways in which presidents have been removed from office. Larry Pfeiffer introduced Mr. Priess and moderator Susan Glasser.


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AUSJEEPOFFROAD.COM Jeep News Australia and New Zealand has 34,291 members, and we have 86 new members this month, a change of +17.2% compared to march.
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Yesterday only, we welcomed 2 new members among our active members. 7 new discussions and 34 new messages were posted.
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Cramlington councillor remains defiant after being targeted by vandals
The Hairy Bikers rave about 'the best fish and chips ever' on visit to Northumberland
Slimmer's life transformed by seven stone weight loss
A nursing assistant has lost more than seven stone in weight after giving up takeaways and ready-made meals.
Friday, 31st December 2021, 10:38 am
Paige Elsender, from Shiremoor, has lost over seven stone.
Paige Elsender weighed in at 23st 6lbs before the Covid-19 pandemic but has trimmed down to 16st 2lbs – and watched her dress size tumble from a 28 to a 14.
"Before losing weight, I didn't really think about what I was eating," she admits. "I never used to make my own meals from scratch.
"I used to go out night clubbing a lot and would eat takeaways when I went out. My biggest downfall was cheese!"
"I make all of my meals from scratch now, which I much prefer – and I will now eat most vegetables, whereas in the past I wouldn't touch anything except carrots."
Now, the 23-year-old from Shiremoor is reaping the rewards of a change in lifestyle.
"I wanted to lose weight because I felt unhealthy, unhappy and I couldn't and I didn't want participate in other things that other people were doing," she explained.
"I was conscious of my weight all of the time. I was scared to sit on wooden benches in beer gardens in case they broke or tipped.
"Being slimmer, I'm a lot more confident, I'm so much happier, I feel free and I don't feel scared to do "normal" things anymore."
She hopes to continue her weight loss journey at the West Allotment branch of Slimming World in the new year – with ice skating and a skydive on her 'to do' list.
"Slimming World was the best thing I have ever done, not just for my physical health but for my mental health as well," said Paige.
"I suffer from bad anxiety and depression which takes a toll on my day to day life, however in losing weight I've gained more confidence to tackle some of the things that make me anxious, such as going out alone.
"I can go into town on my own now, I can get on public transport, I'm able to talk to people and it has given me even more confidence at work as well. I have more energy too. I'd never have done that prior to losing weight."
Construction due to start on major £4.5m retail scheme in Blyth
Safety concerns raised at idea of extra parking near Northumberland beauty spot
Delight as controversial plans to merge two Northumberland schools are scrapped
Northumberland strongman enjoys world championship success


This study, AN ASSESSMENT OF LOAN DEFAULTS AND ITS IMPACTS ON PROFITABILITY (A CASE STUDY OF ECO BANK PLC) contains concise information that will serve as a framework or guide for your project work. The project study is well-researched for academic purposes and are usually provided in complete chapters with adequate References.
A part from the basic objectives of this research thesis, the impartial fulfillment for the award of master degree in Public Administration in the Department of political Science And Defence Studies, Nigerian Defecnce Academy, Kaduna. The thesis was conducted primarily to ascertain the effectiveness of financial incentives to workers motivation in National Board for Technical Education.
The whole research was divided into five chapters. Chapter one deals with the General Introduction, Background to the study, Statement of the Research Problems, Study, Research Questions, Objectives of the study, Hypothesis, Significant of the study, Methodology, Sources of Data Collections, Scope and Limitations of the Study and Definitions of Terms.
While Chapter two highlight Literature Review and Theatrical Frame Work, introduction motivation Concepts, Extrinsic Motivation, Six basic Desires Concepts, Transcendent motivation, Self determination and Self Control, Motivation and Incentives as viewed by various School of Thought, Theoretical Framework and Incentive theory.
However, Chapter three discussed extensively on the Historical Background of National Board for Technical Education, Kaduna. Introduction, Functions of the Board, The Structures of the Board, The Departments of the Board, Major Achievement of the Board, Challenges of the Board, Lingering issues in Federal Polytechnics.
Chapter four, presented and analyzed financial incentives to workers motivation in National Board for Technical Education, Data presentations and Analysis, Presentation of Tables, Pie Chart Computation and Major findings.
Chapter five, highlighted the Summary, Conclusion and Recommendations of the Study, Appendices and Bibliography of the Thesis. The researcher gave some recommendations which we hope will help to minimize the problems and enhance productivity, efficiency and Industrial harmony in the Organization. More so, in identifying the above problems not intented to discredit the present system being in operation in the organization but there are merely views as depicted through and felt in the course of the research carried out.
If researcher's views and suggestions were implemented well, it may definitely lead to greater productivity, job satisfactions and Industrial harmony between the workers and Management of National Board for Technical Education, which will stand the test of time and assist in enhancing workers performance.
In the word of Armstrong (1988), the process of motivation is initiated by the conscious and unconscious recognition of an unsatisfied need. A goal is then established which, it is thought will satisfy the need and of course action is determined that lead towards the attainment of a goal. Management should provide incentive schemes and pay workers on the basis of the result they achieve on the job instead of the more physical routine performance series activities and to retain them on their job making them feel satisfied, a motivationally-oriented wage system must adequately distinguish "Naira" wise between the different levels of efficiency for the people performing essentially job and different job categories and specialization.
In every organization, the management emphasis on high productivity, quality of services, quality workmanship, industrial peace, cooperative labour etc. On the other hand, employees need fair wages, job satisfaction, good working conditions, participation in decision making, self recognition and opportunity for advancement.
Organizations and managers have suffered tremendously in trying to utilize their human resources, they usually encounter frequent industrial conflicts and several unresolved agitations by workers and different categories of employees basically steaming from one form of dissatisfaction or the other. The main point of misunderstanding between management and employees/workers in most cases is found in the arrears of inadequate and inequitable monetary rewards.
Financial incentive as we all know is a process of guiding the conduct and influencing people so that they strives individual or group towards the achievement of group goals. Every employee comes to an organization with one motive, to earn a living and financial incentive play a vital role in the lives of these employees. Taking away financial incentive might jeopardize this individual or the group interest. Management on the other hand, established the organization for the purpose of return of investment and profit making, high productivity, quality of services, industrial peace, cooperative labour and to remain a going concern. Skinner B. F. (1953), states that by providing properly scheduled rewards is possible to influence behaviours.
The objective and purpose of this study is to examine whether or not financial incentives has contributed to workers performance and industrial harmony in National Board for technical Education. This research is by no means exhaustive but will help the establishment to take a second look that financial incentives has a significant role to play in maintaining industrial peace, increase productivity and boost the morale of the employees in an establishment.
It has generally been observed and noted that in a sample group of workers performing the same type of job, some do it better than others. This observation will raise and arouse the notion or questions or psychological tendencies, interest and differences in performance. One school of though holds the view that "differences in performance reflect varying characteristics, abilities and skills on the part of 'workers'. F.B. Skinner, (1985), an Industrial psychologist argues that differences in performance of workers doing the same kind of job, might be as a result of extra monetary rewards attached to the job, conductive working environment or friends they meet in the workplace.
As a result of these possibilities, recognition and thorough understanding of workers needs/wants before adopting any form of motivational techniques such as financial rewards (money) human relations, conducive, working environment, leadership and good supervision among others, becomes apparently important since these factors has different influence and impact on different categories of workers and individuals.
The complexity of human nature, expectation, urges and drives/motives make the art of motivation of workers and employees a critical and complex point for consideration. A definite answer could not be reached since people differ in characteristics, background, traits, and needs. Thus it becomes imperative for the manager to incorporate positive motivational incentive programmes to motivate workers behaviour towards achievement of predetermine goals and objective of the organization.
Motivation is a very important issues in managing people. A happy employee is said to be a motivated employee. So it is important for managers, especially human resource managers to figure out what motivate an employee to excel at his/her work. Workers in any organization need something to keep them working. Most times the salary of the employee is not enough to keep him/her working for an organization due to economic factors and other variables. Sometime also just working for salary is not enough for employees to stay in the organization. An employee needs to be adequately motivated, the absence motivation scheme results to deteriorate in quality of work/performance either on individual or at corporate level. Even in conductive work environment it is generally observed that while some people work willing, others work very willing. The question then is what is responsible for people's motives and attitude to work.
By definition, managers work with and through people to get things done. But people are complex and their motivations are not always easy to understand. It involves the unique feelings, through past experience of individuals as they share a variety of relationships within and outside the organization. Many theories exist about motivation and most of them differ in what they suggest managers should do to obtain the most effective performance from their employees. Most successful managers, however have learned by experience that people are generally very responsive to praise and encouragement-expressed not only in words but also in actions such as financial rewards-and they need to feel successful in their work in order to give their best effort to the organization. Managers who find the key to their employees' inner motivations can tap an immense source of productive energy.
While motivation is essentially a personal experience, managers, in particular, should be keen to find reliable links between motivation and effective performance. They should also be concerned with creating the conditions under which organizational and personal goals may be harmonized. The key feature of motivation is that it determines the extent to which an individual desires to place his/her knowledge and skill at the disposal of others, and more than that to push off the effects of obstacles and difficulties in so doing. This project work examines the motivating power and relevance of financial incentive in boasting the performance of workers.
The general concept of financial incentives is one form of motivating techniques and its indispensability for achievement of desired organizational goals and increase productivity and reward for performance has been a subject of controversy over the years globally generating diverse research arguments, criticisms and assumptions especially in developing country like ours.
Although many researches had been conducted on this concept, there are many avenues not yet explored and considered as per the complexities to the time understanding of what actually motivate the individuals in the work place. Organizations and managers have suffered tremendously in trying to utilize their human resources, they usually encounter frequent industrial conflicts and several unresolved agitations by workers and different categories of employees basically steaming from one form of dissatisfaction or the other. The main point of misunderstanding between management and employees/workers in most cases is found in the arrears of inadequate and inequitable monetary rewards.
One of the problems of workers in National Board for Technical Education is financial incentives which led to workers dissatisfaction and low productivity. It is evident here that the mode of financial incentives used by National Board for Technical Education has not been effective.
Secondly, there is correlation between financial incentives and workers productivity in National Board for Technical Education which the management is not implementing.
Thirdly, the problems militating against National Board for Technical Education staff is financial incentives because there are not adequately provided. Another problem is delay in paying those who have performed their duties.
Even in most conductive work environment, it is generally observed that; while some people work willingly, others work unwillingly, the question then is what is responsible for people's motive/attitude to work? As one psychologist puts it, "One of the most powerful positive tools that motivate people at work is financial incentives (money) at the prime stage.
What types of motivation or financial incentive do workers received at National Board for Technical Education?
Is there any correlation between financial incentives for workers and productivity in National Board for Technical Education?
What are the problems militating against financial incentives of staff of National Board for Technical Education?
How can these weaknesses be overcome to enhance motivation and productivity National Board for Technical Education?
The objective of this study is to examine and highlight the negative impact of financial incentives to National Board for Technical Education staff. – It is expected that the findings of this research will be beneficial to policy makers, the Nigerian Public Sector and National Board for Technical Education.
To analyze the objectives of this research to know whether or not financial incentives are the highest/greatest motivators to workers performance in National Board for Technical Education.
The study is aimed at adding to the existing body of knowledge on the subject matter and serve as a useful reference source for researchers in the field.
This study is not intended to find faults with any motivation techniques adopted by the National Board for Technical Education or negate the idea but to establish the effects and appraisal of financial rewards to their employees contribution in terms of productivity/efficiency being an indispensable management tool for achieving desired organizational goals and objectives.
Lack of financial incentives has been the major impediment to workers motivation in National Board for Technical Education.
Financial incentive has been the major boost/influence to workers motivation in National Board for Technical Education.
Financial incentive can be considered by management as a indispensable tool for workers motivation in National Board for Technical Education.
Every organization in Nigeria today whether profit or non-profit oriented, is most concerned continuously with how to meet its organizational goals. A successful motivation strategy would result not only through the attainment of corporate objectives but through individual recognition or perceptions, aspirations, ability, skills and motives, desires and satisfaction. These of course, will also enhance increase in aggregate output level. Nigeria today moved far ahead from period when inducement or threat of any kind seen as effective tools of management for rapid development and growing economy.
The researchers' choice on the topic "Appraisal of the relevance of financial incentive to workers motivation" therefore emanates from the fact that early available research on the topic seems to have conducted based on developed nations with totally different socio economic, political and other background different from ours which to some extent still is under-affluent economy.
We have witnessed in the past few years in our industries, the increased rate of industrial disharmony (strike, lock-out etc) with frequent demand for higher wages more than other countries both in the public and private sectors respectively. This of course indicates that a lot is yet to be done in human resource management particularly in the aspect of employee's motivation (Oshomole, 2007). This study therefore is meant to contribute to the unresolved controversy as to whether or not financial remuneration is a positive incentive in motivating human behaviour at work.
For the purpose of gathering information for this research project, secondary method of data collection was used.
Education, Annual Report, Staff Manual, Workshop, Seminar papers, Conferences, Paper presentation at NBTE floras and journals, Internets, policy Papers among others were consulted.
The total population and staff strength of National Board for Technical Education Kaduna constituted a population of 308 workers and this number served as the population and sample size of this study.
Questionnaires was designed and administered to the different categories of National Board for Technical Education workers. Questions were intended to obtain information about the authenticity of the relevance of financial incentives in motivating National Board for Technical Education employees.
The researcher could not have full access to some of the information needed from the management due to the fact that the custodians of such information could not be reached.
Bureaucratic bottlenecks created a big problem because of continuous visit to the establishment due to unavoidable absence of people in the right position that gave birth to unnecessary time wastage and delays in completing the project work.
Much spending going up and down without contacting the appropriate personnel on seat, typing cost and increase in materials needed. Despite all these constraints.
Despite the fact that a questionnaire was designed to eliminate bias and misunderstanding, some employees refuse to complete the questionnaires form, due to nonchalant attitude and forgetfulness.
Intrinsic and Extrinsic motivations refers to motivation that is driven by an interest or enjoyment in the task itself and exist within the individual rather than relying on any external pressure. While intrinsic motivation has been studied by social and educational psychologists since the early 1970s. research has found that it is usually associated with high educational achievement and enjoyment by students. Expectations of intrinsic motivation have been given in the context of Fritz Heider, (1873), attribution theory. Bandura, (1980), work on self-efficiency and Dedi and Ryan (1964), cognitive evaluation theory (see determination theory) students are likely to be intrinsically motivated if they.
Attribute their educational results to internal factors that they can control (e.g. amount of effort they put in).
Believe they can be effective agents in reading and reaching their desired goal (e.g. the result are determined by luck but hard work).
This type of motivation comes from outsides of the individual. Common extrinsic motivations are rewards like money and grades, coercion and threat of punishment. Competition is in general extrinsic because it encourages the performer to win and beat others not to enjoy the intrinsic rewards of the activity. A crowd cheering on the individual and trophies are also extrinsic incentives. Social psychologist has indicated that extrinsic rewards can lead to over-justification and a subsequent reduction intrinsic motivation.


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By Best Buy Company News
28 Apr: Best Buy stands with AAPI employees, communities
Asian American and Pacific Islander Heritage Month is a time to recognize and celebrate the vibrant role the AAPI community plays in our nation's culture and heritage. However, we also must acknowledge the struggle and pain taking place within that community right now.
There has been a dramatic rise in anti-Asian racist incidents nationwide since the start of the COVID-19 pandemic. That ranges from racial slurs to extreme violence in some cases.
Especially now, Best Buy stands with our AAPI employees and communities.
By Best Buy Lifestyle
28 Apr: Living my values: Best Buy leaders celebrate their Asian American heritage
During Asian American and Pacific Islander (AAPI) Heritage Month this May, we want to take the time to reflect on the significant contributions and achievements AAPI Americans have made — and continue to make — to our country, our communities and Best Buy.
This observance comes at a time that has been significantly difficult for the AAPI community, with anti-Asian hate crimes on the rise since the COVID-19 pandemic began. Now, it's more important than ever to share and celebrate the voices of the AAPI community.
We're proud to highlight four AAPI leaders who shared how their family, culture and experiences have shaped who they are today.
By Emily Gaylord Lifestyle
28 Apr: Creativity, Connection Fuel This Best Buy Employee's Passion
Since he was young, Paul Asao has always loved beautiful things.
He credits this to the creatives in his life who showed him how to express a passion for arts, including his mother, Rose. She was a talented artist who used art, including sumi-e paintings (Japanese ink painting) and calligraphy, to honor her Japanese American heritage.
Now as a creative director for Best Buy Creative Services, Paul is constantly creating and using art to tell the Best Buy story.
"A close friend of mine in the advertising industry once told me, 'Never stop doing what you like or want to do,'" Paul said.
28 Apr: She's proud to carry on her family's trailblazing legacy
If you've met Jen Teves, you've met her grandmother, Vicenta. The two were so close that Jen can see how her grandmother, who died in 2011, shows up in her day-to-day life.
When Vicenta, a teacher in the Philippines, taught Jen math as a child, she wasn't allowed to have calculators or count on her fingers. She would put her hands behind her back and work the problems out in her head.
Jen, a research director at Best Buy, still uses these skills and others her grandmother taught her.
By Kaylie Brazil Company News
28 Apr: Asian ERG brings community, bridges cultures
Best Buy employees typically join Employee Resource Groups (ERGs) for allyship, belonging and community — sometimes referred to as the ABCs of ERGs. And the Asian ERG's members get all of that and then some.
Best Buy's Asian ERG (AERG) has almost 1,000 members and aims to represent and support everyone involved. That includes highlighting more than 48 countries and their respective cultural celebrations, from Lunar New Year and Diwali to Hmong New Year and Philippine Independence Day.
The group offers an outlet for purposeful interactions and a chance to learn more from one another.


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Arvid Bertil Högbom, född 31 augusti 1888 i Uppsala, död 25 september 1962 i Danderyds församling, var en svensk geolog och företagsledare.

Bertil Högbom var son till Arvid Högbom och bror till Ivar Högbom. Efter mogenhetsexamen i Uppsala 1907 studerade han vid Uppsala universitet, blev 1910 filosofie magister, 1913 filosofie licentiat och 1914 filosofie doktor där. 1914–1918 var han anställd hos A. Johnson & co. i Stockholm, 1918–1923 var han direktör för AB Nordsvenska malmfält och anställdes 1923 i Grängesbergsbolaget, från 1925 som dess representant i Berlin och direktör för Schwedenerz G. m. b. H.. Högboms skrifter behandlade huvudsakligen geologiska, geografiska och ekonomiska ämnen. Som ung student 1908 deltog han i Gerard De Geers expedition till Spetsbergen för insamling av fossil och 1910 och 1911 expeditioner för undersökning av samma ögrupps kolförekomster. 1911–1912 färdades Högbom i Siam där han ägnade sig åt vetenskaplig och praktisk geologi, beskrivningar därifrån utgavs 1914 under titeln Färder i Siam. 1912 undersökte han kolförekomster i Uralbergen och 1913 kompletterade han i de skandinaviska högfjällen det material av iakttagelser rörande frostens verkningar och flytjordsfenomenen, som han tidigare studerat på Svalbard, information som sedan kom att användas för doktorsavhandlingen Über die geologische Bedeutung des Frostes. Under sina arbeten i Lappland upptäckte Högbom huvudtillgångarna av järnmalm inom Masugnsbyfälten och den även betydande järnmalmsförekomsten Vieto väst om Kiruna.

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Svenska geologer under 1900-talet
Personer inom Sveriges näringsliv under 1900-talet
Forskare från Uppsala
Födda 1888
Avlidna 1962
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Animals with Opinions: Gerald's Stunt Double!!
yes that's right!! gerald i have your stunt double. you don't deserve it but i couldn't resist. he looks just like you. i think you will be pleased. i'll post a pic of him in the afternoon!


Minister for Education and Skills Ruairi Quinn TD has announced a second round of construction works for 13 schools across Donegal including Glenswilly National School, Newmills, Mulroy College Milford and Scoil Cholmcille, Letterkenny.
Siobhan McLaughlin, a Labour election candidate in the Letterkenny/Milford electoral area, has welcomed the news saying she is 'delighted' to see Donegal included in the allocation of the funding and in particular three schools in her electoral area.
Funding will contribute to improving the school buildings. Ms. McLaughlin congratulated the schools on their success in accessing the funds, and noted that the jobs would be a 'welcome bonus' to the local construction workforce over the summer months.