Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b7dq)

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=-43/8, b>=a

For fixed z and a=-43/8, b=-39/8

http://functions.wolfram.com/07.23.03.b7dq.01

Input Form

Hypergeometric2F1[-(43/8), -(39/8), -(19/4), z] == (6688 - 37312 z + 85558 z^2 - 102582 z^3 + 67114 z^4 - 22538 z^5 + (6688 - 40656 z + 103378 z^2 - 141115 z^3 + 109781 z^4 - 47345 z^5 + 9269 z^6)/Sqrt[1 - z])/(6688 2^(3/4) (1 + Sqrt[1 - z])^(1/4))

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]