Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.by7o)

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=1/8, b>=a

For fixed z and a=1/8, b=47/8

http://functions.wolfram.com/07.23.03.by7o.01

Input Form

Hypergeometric2F1[1/8, 47/8, -(9/2), z] == (1/(45997056 (1 - z)^(21/2))) (2 Sqrt[1 - z] (22998528 - 234457216 z + 1083681570 z^2 - 3010814333 z^3 + 5685254517 z^4 - 8772051834 z^5 + 6166646884 z^6 - 3293535945 z^7 + 1186520181 z^8 - 256455584 z^9 + 25116784 z^10) Cos[ArcSin[Sqrt[z]]/4] + Sqrt[z] (11499264 - 120822128 z + 576947479 z^2 - 1660052945 z^3 + 3249577356 z^4 - 23017019570 z^5 + 15360294367 z^6 - 7712617773 z^7 + 2623216750 z^8 - 538027952 z^9 + 50233568 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]