Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c3u7)

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=11/8, b>=a

For fixed z and a=11/8, b=45/8

http://functions.wolfram.com/07.23.03.c3u7.01

Input Form

Hypergeometric2F1[11/8, 45/8, -(9/2), z] == -((1/(7691264 (1 - z)^(23/2))) (Sqrt[1 - z] (-7691264 + 99986432 z - 625039668 z^2 + 2585600589 z^3 - 8753990025 z^4 + 40858232646 z^5 + 47452849418 z^6 - 3989719127 z^7 + 708456051 z^8 - 98254252 z^9 + 6970288 z^10) Cos[(3 ArcSin[Sqrt[z]])/4] + Sqrt[z] (-5768448 + 75831056 z - 479189997 z^2 + 2001104226 z^3 - 6810153955 z^4 + 63839849544 z^5 + 49365020589 z^6 - 4332101014 z^7 + 756711891 z^8 - 101739396 z^9 + 6970288 z^10) Sin[(3 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]