Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.by7l)

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.by7l.01

Input Form

Hypergeometric2F1[1/8, 47/8, -(11/2), -z] == (1/(32124928 (1 + z)^(23/2))) (Sqrt[1 + z] (32124928 + 358667520 z + 1828588320 z^2 + 5636265713 z^3 + 11750302031 z^4 + 17770044812 z^5 + 22974421470 z^6 + 13867392985 z^7 + 6478931731 z^8 + 2073716282 z^9 + 403190480 z^10 + 35881120 z^11) Cosh[ArcSinh[Sqrt[z]]/4] - 2 Sqrt[z] (4015616 + 46088320 z + 242050666 z^2 + 770318783 z^3 + 1661857548 z^4 + 2602188329 z^5 + 14606545130 z^6 + 8435721057 z^7 + 3733816816 z^8 + 1135413191 z^9 + 210565520 z^10 + 17940560 z^11) 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]