Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.0090)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

Specialized values

For fixed a, b, z

http://functions.wolfram.com/07.23.03.0090.01

Input Form

Hypergeometric2F1[a, b, a + b + 3/2, z] == ((1/(2 a + 1)) Gamma[a + b + 3/2] (Sqrt[-z] LegendreP[b - a - 1/2, 1/2 - a - b, 3, Sqrt[1 - z]] - 2 b LegendreP[b - a + 1/2, -(1/2) - a - b, 3, Sqrt[1 - z]]))/ (-(z/4))^((1 + 2 a + 2 b)/4) /; !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]