Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c9z1)

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=25/8, b>=a

For fixed z and a=25/8, b=47/8

http://functions.wolfram.com/07.23.03.c9z1.01

Input Form

Hypergeometric2F1[25/8, 47/8, -(9/2), z] == -((1/(45997056 (1 - z)^(27/2))) (Sqrt[1 - z] (-45997056 + 787060736 z - 6811731060 z^2 + 41971983481 z^3 - 237353568878 z^4 + 2261970230871 z^5 + 7913402564076 z^6 + 3947119093335 z^7 + 200376897858 z^8 - 8294400519 z^9 + 291396756 z^10) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (-11499264 + 200358704 z - 1762894639 z^2 + 10999919441 z^3 - 62405911799 z^4 + 17609590473933 z^5 + 29477377286559 z^6 + 9223327414083 z^7 + 204487673523 z^8 - 8440098897 z^9 + 291396756 z^10) 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]