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

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=-31/8, b>=a

For fixed z and a=-31/8, b=47/8

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

Input Form

Hypergeometric2F1[-(31/8), 47/8, -(11/2), -z] == (1/(405504 (1 + z)^(15/2))) (Sqrt[1 + z] (405504 + 1172736 z + 484640 z^2 - 430911 z^3 + 582829 z^4 - 1208207 z^5 + 7005999 z^6 + 44326810 z^7 + 79276208 z^8 + 67354848 z^9 + 28410624 z^10 + 4815360 z^11) Cosh[ArcSinh[Sqrt[z]]/4] - 2 Sqrt[z] (50688 + 162432 z + 99658 z^2 - 50479 z^3 + 56680 z^4 - 122122 z^5 + 11245718 z^6 + 38566561 z^7 + 54851632 z^8 + 40479120 z^9 + 15409152 z^10 + 2407680 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]