\begin{definition}[Definition:Half-Range Fourier Sine Series/Formulation 2]
Let $\map f x$ be a real function defined on the interval $\openint a b$.
Then the ''' half-range Fourier sine series''' of $\map f x$ over $\openint a b$ is the series:
:$\ds \map f x \sim \sum_{m \mathop = 1}^\infty B_m \sin \frac {m \pi \paren {x - a} } {b - a}$
where for all $n \in \Z_{> 0}$:
:$B_m = \ds \frac 2 {b - a} \int_a^b \map f x \sin\frac {m \pi \paren {x - a} } {b - a} \rd x$
\end{definition}