Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4y8)

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.b4y8.01

Input Form

Hypergeometric2F1[-(47/8), -(9/8), 11/2, z] == (1/(4033941122312475 z^(9/2))) (1024 (Sqrt[z] (15012928 - 247981400 z + 2132740573 z^2 - 14323070554 z^3 + 4079011822299 z^4 + 5219524722888 z^5 + 353974325235 z^6 - 50149103586 z^7 + 8093876133 z^8 - 970631508 z^9 + 59487120 z^10) Cos[ArcSin[Sqrt[z]]/4] + (1/Sqrt[1 - z]) ((-60051712 + 1033211152 z - 9207985025 z^2 + 63078324987 z^3 - 597191186761 z^4 - 1070156881593 z^5 + 1280856648297 z^6 + 378095483265 z^7 - 54078430659 z^8 + 8571755997 z^9 - 1000375068 z^10 + 59487120 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]