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

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=-39/8, b>=a

For fixed z and a=-39/8, b=45/8

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

Input Form

Hypergeometric2F1[-(39/8), 45/8, -(23/4), z] == ((1 + Sqrt[1 - z])^(3/4) (2 (82526576 - 86114688 z - 71774043 z^2 - 71585195 z^3 - 86233791 z^4 - 146757429 z^5 + 12646227594 z^6 - 35444762496 z^7 + 39904989696 z^8 - 20809383936 z^9 + 4191289344 z^10) + (1/Sqrt[1 - z]) (165053152 - 254755952 z - 78065042 z^2 - 60183497 z^3 - 78621929 z^4 - 178198475 z^5 - 27381917745 z^6 + 111757787856 z^7 - 183757406976 z^8 + 153438928896 z^9 - 65038516224 z^10 + 11176771584 z^11)))/ (330106304 2^(3/4) (-1 + z)^6)

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]