Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bc7x)

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=-37/8, b>=a

For fixed z and a=-37/8, b=39/8

http://functions.wolfram.com/07.23.03.bc7x.01

Input Form

Hypergeometric2F1[-(37/8), 39/8, 23/4, z] == (1/(92714195655 z^5)) (16 2^(3/4) (1 + Sqrt[1 - z])^(1/4) (17185168 + 4296292 z + 8494941 z^2 + 26572845 z^3 + 180262927 z^4 - 1798323309 z^5 + 4278404064 z^6 - 4587019008 z^7 + 2363412480 z^8 - 477954048 z^9 - (1/Sqrt[1 - z]) (17185168 - 4296292 z + 4198649 z^2 + 20714265 z^3 + 164974823 z^4 - 4790263657 z^5 + 17781100356 z^6 - 29028037632 z^7 + 24690631680 z^8 - 10768023552 z^9 + 1911816192 z^10)))

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]