Gauss hypergeometric function 2F1: Identities (formula 07.23.17.0147)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Identities

Functional identities

Generic general cases

http://functions.wolfram.com/07.23.17.0147.01

Input Form

Hypergeometric2F1[a, b, c, z] == E^(2 I (c - a - b) Pi) (1/(1 - z))^a Hypergeometric2F1[a, -b + c, c, z/(z - 1)] - ((2 I E^(I (c - a - b) Pi) Pi Gamma[c])/(Gamma[1 + a + b - c] Gamma[-a + c] Gamma[-b + c])) Hypergeometric2F1[a, b, 1 + a + b - c, 1 - z] /; IntervalMemberQ[Interval[{1, Infinity}], z]

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

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]