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   A051149 Continued fraction for BesselK(1,2)/BesselK(0,2). 4
  
  %I
  
  %S 1,4,2,1,1,2,8,1,6,1,4,2,1,8,1,1,7,1,6,4,2,1,6,1,1,2,1,1,1,2,5,1,3,3,
  
  %T 1,3,1,8,1,1,1,1,1,2,3,8,3,29,1,7,1,57,1,121,2,14,2,8,1,1,16,1,3,1,5,
  
  %U 1,5,1,4,17,1,5,6,1,3,2,9,7,1,4,4,1,1,16,3,5,2,1,2,1
  
  %N Continued fraction for BesselK(1,2)/BesselK(0,2).
  
  %H Harry J. Smith, <a href="/A051149/b051149.txt">Table of n, a(n) for n = 0..2000</a>
  
  %H <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
  
  %H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
  
  %e 1.228036929818907975742672452...
  
  %e BesselK(1,2)/BesselK(0,2) = 1 + 1/(4 + 1/(2 + 1/(1 + 1/(1 + ...)))). - _Harry J. Smith_, Apr 29 2009
  
  %t ContinuedFraction[BesselK[1,2]/BesselK[0,2],90] (* _Harvey P. Dale_, Sep 07 2018 *)
  
  %o (PARI) { allocatemem(932245000); default(realprecision, 2100); x=contfrac(besselk(1,2)/besselk(0,2)); for (n=1, 2001, write("b051149.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, Apr 29 2009
  
  %Y Cf. A051148, A000994, A000995.
  
  %K nonn,cofr
  
  %O 0,2
  
  %A _N. J. A. Sloane_, E. M. Rains
  
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  Last modified June 25 09:48 EDT 2019. Contains 324347 sequences. (Running on oeis4.)
explanation: The provided text is an entry from the On-Line Encyclopedia of Integer Sequences (OEIS) for the sequence A051149, which represents the continued fraction for the ratio of Bessel functions BesselK(1,2)/BesselK(0,2). The entry includes the sequence itself, references, and a few examples. It does not contain a specific math question or a question and answer.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: This site is supported by donations to The OEIS Foundation.
  
   Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
   A051149 Continued fraction for BesselK(1,2)/BesselK(0,2). 4
  
  %I
  
  %S 1,4,2,1,1,2,8,1,6,1,4,2,1,8,1,1,7,1,6,4,2,1,6,1,1,2,1,1,1,2,5,1,3,3,
  
  %T 1,3,1,8,1,1,1,1,1,2,3,8,3,29,1,7,1,57,1,121,2,14,2,8,1,1,16,1,3,1,5,
  
  %U 1,5,1,4,17,1,5,6,1,3,2,9,7,1,4,4,1,1,16,3,5,2,1,2,1
  
  %N Continued fraction for BesselK(1,2)/BesselK(0,2).
  
  %H Harry J. Smith, <a href="/A051149/b051149.txt">Table of n, a(n) for n = 0..2000</a>
  
  %H <a href="/index/Be#Bessel">Index entries for sequences related to Bessel functions or polynomials</a>
  
  %H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
  
  %e 1.228036929818907975742672452...
  
  %e BesselK(1,2)/BesselK(0,2) = 1 + 1/(4 + 1/(2 + 1/(1 + 1/(1 + ...)))). - _Harry J. Smith_, Apr 29 2009
  
  %t ContinuedFraction[BesselK[1,2]/BesselK[0,2],90] (* _Harvey P. Dale_, Sep 07 2018 *)
  
  %o (PARI) { allocatemem(932245000); default(realprecision, 2100); x=contfrac(besselk(1,2)/besselk(0,2)); for (n=1, 2001, write("b051149.txt", n-1, " ", x[n])); } \\ _Harry J. Smith_, Apr 29 2009
  
  %Y Cf. A051148, A000994, A000995.
  
  %K nonn,cofr
  
  %O 0,2
  
  %A _N. J. A. Sloane_, E. M. Rains
  
  Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
  Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
  The OEIS Community | Maintained by The OEIS Foundation Inc.
  
  Last modified June 25 09:48 EDT 2019. Contains 324347 sequences. (Running on oeis4.)
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is an entry from the On-Line Encyclopedia of Integer Sequences (OEIS) for the sequence A051149, which represents the continued fraction for the ratio of Bessel functions BesselK(1,2)/BesselK(0,2). The entry includes the sequence itself, references, and a few examples. It does not contain a specific math question or a question and answer.
  
  Label: no-question