Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bex8)

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=-9/8

http://functions.wolfram.com/07.23.03.bex8.01

Input Form

Hypergeometric2F1[-(31/8), -(9/8), 9/2, z] == (1/(377207225967 z^(7/2))) (256 (Sqrt[z] (-57040 + 769327 z - 5877259 z^2 + 1528970306 z^3 + 1590243370 z^4 + 78323635 z^5 - 6402591 z^6 + 390572 z^7) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) ((228160 - 3234168 z + 25605969 z^2 - 237937369 z^3 - 316285306 z^4 + 456353910 z^5 + 81476109 z^6 - 6597877 z^7 + 390572 z^8) Sin[ArcSin[Sqrt[z]]/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]