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

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.bftj.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) Cos[ArcSin[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) Sin[ArcSin[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]