Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.0105)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

Specialized values

For fixed a, b, z

http://functions.wolfram.com/07.23.03.0105.01

Input Form

Hypergeometric2F1[a, b, 2 b, z] == (((2^(2 b) Exp[Pi I (a - b)])/Sqrt[Pi]) (Gamma[b + 1/2]/Gamma[2 b - a]) (1 - z)^((b - a)/2) LegendreQ[b - 1, b - a, 3, 2/z - 1])/z^b /; !IntervalMemberQ[Interval[{-Infinity, 0}], 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)

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]