Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5sj)

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.b5sj.01

Input Form

Hypergeometric2F1[-(47/8), 47/8, -(11/2), z] == -((1/(135168 (1 - z)^(11/2))) (Sqrt[1 - z] (-135168 - 168192 z - 262496 z^2 - 506077 z^3 - 1283854 z^4 - 4980261 z^5 - 51492584 z^6 + 503250264 z^7 - 1269328896 z^8 + 1441237248 z^9 - 782014464 z^10 + 165648384 z^11) Cos[ArcSin[Sqrt[z]]/4] + 4 Sqrt[z] (-8448 - 7872 z - 11999 z^2 - 24453 z^3 - 66924 z^4 - 279851 z^5 - 52127735 z^6 + 250041330 z^7 - 475637184 z^8 + 452884608 z^9 - 216209664 z^10 + 41412096 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]