Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c9z6)

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.c9z6.01

Input Form

Hypergeometric2F1[25/8, 47/8, -(7/2), -z] == (1/(1277696 (1 + z)^(25/2))) ((-Sqrt[1 + z]) (-1277696 - 22074480 z - 203443855 z^2 - 1526662766 z^3 - 18019284657 z^4 + 76863097296 z^5 - 45067543905 z^6 + 2646114570 z^7 + 122666433 z^8 + 4776996 z^9) Cosh[ArcSinh[Sqrt[z]]/4] + Sqrt[z] (-319424 - 5618440 z - 52543109 z^2 - 396851522 z^3 - 152589375987 z^4 + 301187085984 z^5 - 108523113915 z^6 + 2706850662 z^7 + 125054931 z^8 + 4776996 z^9) Sinh[ArcSinh[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]