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MathGroup Archive 1998

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Re: hypergeometric function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg12913] Re: [mg12857] hypergeometric function
  • From: "Jrgen Tischer" <jtischer at col2.telecom.com.co>
  • Date: Wed, 24 Jun 1998 03:44:34 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Selber Hello,

M. Abramowitz, I Stegun ed, Handbook of Mathematical Functions, Dover
1965,
p. 256:
Pochhammer's Symbol,
(z)_n=z(z+1)(z+2)...(z+n-1)=Gamma(z+n)/Gamma(z).

Jrgen


-----Original Message-----
From: Klamser <Klamser at t-online.de>
To: mathgroup at smc.vnet.net
Subject: [mg12913] [mg12857] hypergeometric function


>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;
>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??
>
>Greetings, Peter Klamser
>
>



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