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

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=-31/8, b>=a

For fixed z and a=-31/8, b=45/8

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

Input Form

Hypergeometric2F1[-(31/8), 45/8, -(23/4), z] == ((1 + Sqrt[1 - z])^(3/4) (-165053152 + 498747568 z - 256007070 z^2 - 201607043 z^3 - 196525315 z^4 - 246353289 z^5 + 9557450301 z^6 - 21603473760 z^7 + 20539613952 z^8 - 9292124160 z^9 + 1654456320 z^10 + (1/Sqrt[1 - z]) (2 (-82526576 + 290637072 z - 242374605 z^2 - 62815566 z^3 - 44222622 z^4 - 60929232 z^5 - 5306339101 z^6 + 18313140870 z^7 - 25910983296 z^8 + 18947563008 z^9 - 7136870400 z^10 + 1102970880 z^11))))/(330106304 2^(3/4) (-1 + 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]