Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c9wl)

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=45/8

http://functions.wolfram.com/07.23.03.c9wl.01

Input Form

Hypergeometric2F1[25/8, 45/8, -(11/2), -z] == (1/(315392 (1 + z)^(113/8))) ((315392 + 5453056 z + 46370016 z^2 + 264876225 z^3 + 1203642309 z^4 + 5285725081 z^5 + 39635945349 z^6 - 133969904949 z^7 + 66214716855 z^8 - 4474850261 z^9 - 121874401 z^10 - 3569232 z^11) Cos[ArcTan[Sqrt[z]]/4] + 2 Sqrt[z] (39424 + 669312 z + 5590326 z^2 + 31415781 z^3 + 141069082 z^4 + 618988643 z^5 - 49495554348 z^6 + 58008129531 z^7 - 11912985294 z^8 + 15094877 z^9 + 446154 z^10) Sin[ArcTan[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]