Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4y4)

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=-9/8

http://functions.wolfram.com/07.23.03.b4y4.01

Input Form

Hypergeometric2F1[-(47/8), -(9/8), 7/2, z] == (1/(367796650683 z^(5/2))) (64 (Sqrt[z] (402132 - 8076151 z + 5903144675 z^2 + 11784926414 z^3 + 1126704810 z^4 - 219013771 z^5 + 46393823 z^6 - 7065212 z^7 + 535920 z^8) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) ((-1608528 + 33410467 z - 647365498 z^2 - 2585018167 z^3 + 2168047456 z^4 + 1230833109 z^5 - 241361026 z^6 + 49859439 z^7 - 7333172 z^8 + 535920 z^9) 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]