Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b4y9)

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.b4y9.01

Input Form

Hypergeometric2F1[-(47/8), -(9/8), 11/2, -z] == (1024 (Sqrt[z] Sqrt[1 + 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) Cosh[ArcSinh[Sqrt[z]]/4] - (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) Sinh[ArcSinh[Sqrt[z]]/4]))/ (4033941122312475 z^(9/2) Sqrt[1 + z])

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]