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MathGroup Archive 1998

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Re: hypergeometric function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg12895] Re: hypergeometric function
  • From: "Stephen P Luttrell" <luttrell at signal.dra.hmg.gb>
  • Date: Wed, 24 Jun 1998 03:44:19 -0400
  • Organization: Defence Evaluation and Research Agency
  • References: <6m7fol$gq2@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Klamser wrote in message <6m7fol$gq2 at smc.vnet.net>...
>Hello,
>
>in the Online-Help of Mathematica or in the Mathematica Book under
>Page #750 I can find the hypergeometric function Hypergeometric2F1[a,
>b, c, z]. I do not understand the definition:
>
>It say's:
>
>\!\(\*FormBox[
>&nbsp; RowBox[{\(\[Null]\_2\), \(F\_1\), \((a, b; c; z)\), "=",
>&nbsp;&nbsp;&nbsp; UnderoverscriptBox["\[Sum]", \(k = 0\),
>"\[Infinity]", &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
>LimitsPositioning->True], \(\(\((a)\)\_k\) \((b)\)\_k\), "/",
>&nbsp;&nbsp;&nbsp; \(\((c)\)\_k\), " ", \(z\^k\), "/", \(k!\), "
>"}], TraditionalForm]\)
>
>The Sum Function uses the contsnts a, b and c wit the Index k. What
>does that mean??


The notation (a)k, where the k is a subscript, means
Gamma(a+k)/Gamma(a), where Gamma(x) is the standard gamma function. See
page xliii of "Table of Integrals, Series, and Products" by Gradshteyn
and Ryzhik

=============================================================

Stephen P Luttrell
luttrell at signal.dera.gov.uk
Adaptive Systems Theory                           01684-894046 (phone)
Room EX21, DERA                                    01684-894384 (fax)
Malvern, Worcs, WR14 3PS, U.K.
http://www.dera.gov.uk/cis5pip/Welcome.html



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