Regularized hypergeometric function 2F1: Primary definition (formula 07.24.02.0004)

Hypergeometric2F1Regularized

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1Regularized[a,b,c,z]

Primary definition

Complete definition

http://functions.wolfram.com/07.24.02.0004.01

Input Form

Hypergeometric2F1Regularized[a, b, c, z] == (Pi/Sin[Pi (b - a)]) (((1/(Gamma[b] Gamma[c - a])) Sum[(Pochhammer[a, k] Pochhammer[a - c + 1, k])/ (k! Gamma[a - b + 1 + k])/z^k, {k, 0, Infinity}])/(-z)^a - ((1/(Gamma[a] Gamma[c - b])) Sum[(Pochhammer[b, k] Pochhammer[b - c + 1, k])/ (k! Gamma[b - a + 1 + k])/z^k, {k, 0, Infinity}])/(-z)^b) /; Abs[z] > 1 && !Element[a - b, Integers]

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQRegularized[{},{b},z]
HypergeometricPFQRegularized[{a₁},{b₁},z]
HypergeometricPFQRegularized[{a₁,...,a_p},{b₁,...,b_q},z]