Gauss hypergeometric function 2F1: Representations through more general functions (formula 07.23.26.0220)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Representations through more general functions

Through Meijer G

Generalized cases involving algebraic functions with squares in arguments

http://functions.wolfram.com/07.23.26.0220.01

Input Form

(z + Sqrt[1 + z^2])^(1 - c - a) Hypergeometric2F1[a, 1, c, (-z + Sqrt[1 + z^2])/(z + Sqrt[1 + z^2])] == ((c - 1)/(2 Sqrt[Pi])) MeijerG[{{(3 - a - c)/2}, {(1 - a + c)/2, (a + c - 1)/2}}, {{0, 1/2, (c - a - 1)/2}, {}}, z, 1/2] /; Re[z] > 0

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)

2001-10-29

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]