Gauss hypergeometric function 2F1: Identities (formula 07.23.17.0074)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Identities

Functional identities

Relations including three Kummer's solutions

http://functions.wolfram.com/07.23.17.0074.01

Input Form

Hypergeometric2F1[a, b, c, z] == (((Gamma[1 - b] Gamma[1 + a - c])/(Gamma[1 + a - b] Gamma[1 - c])) Hypergeometric2F1[a, -b + c, 1 + a - b, 1/(1 - z)])/(1 - z)^a + ((Gamma[1 - b] Gamma[1 + a - c] Gamma[c])/(Gamma[a] Gamma[2 - c] Gamma[-b + c])) (1 - z)^(1 - c) (-1 + z)^(-1 + c) z^(1 - c) Hypergeometric2F1[1 + b - c, 1 + a - c, 2 - c, z] /; !IntervalMemberQ[Interval[{0, 1}], 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)

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]