Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5th)

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=-47/8, b>=a

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

http://functions.wolfram.com/07.23.03.b5th.01

Input Form

Hypergeometric2F1[-(47/8), 47/8, 11/2, -z] == (1024 (4 Sqrt[z] Sqrt[1 + z] (5264 - 22278 z + 99264 z^2 - 616781 z^3 + 193352588 z^4 + 1288880637 z^5 + 3489326478 z^6 + 4971498048 z^7 + 3948835968 z^8 + 1661780736 z^9 + 289884672 z^10) Cosh[ArcSinh[Sqrt[z]]/4] - (84224 - 298544 z + 1336257 z^2 - 8744021 z^3 + 149602739 z^4 + 2390354945 z^5 + 10407688368 z^6 + 22296034728 z^7 + 27025244928 z^8 + 18973963008 z^9 + 7226892288 z^10 + 1159538688 z^11) Sinh[ArcSinh[Sqrt[z]]/4]))/ (751899556815 z^(9/2) Sqrt[1 + z])

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]