Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bh6x)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a<0

For fixed z and a=-29/8, b>=a

For fixed z and a=-29/8, b=39/8

http://functions.wolfram.com/07.23.03.bh6x.01

Input Form

Hypergeometric2F1[-(29/8), 39/8, 15/4, z] == (1/(148542855 z^3)) (4 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (10556 + 81055 z + 909701 z^2 - 12793168 z^3 + 34353792 z^4 - 34265088 z^5 + 11714560 z^6 + (1/Sqrt[1 - z]) (-10556 - 75777 z - 867854 z^2 + 31826667 z^3 - 136255648 z^4 + 227800320 z^5 - 169275392 z^6 + 46858240 z^7)))

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]