Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.bb4m)

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=-19/4, b>=a

For fixed z and a=-19/4, b=41/8

http://functions.wolfram.com/07.23.03.bb4m.01

Input Form

Hypergeometric2F1[-(19/4), 41/8, -(39/8), z] == -((1/(2363595 (1 - z)^(21/4))) (-2363595 + 606050 z + 615825 z^2 + 1071000 z^3 + 2873850 z^4 + 15272460 z^5 - 496354950 z^6 + 1481186200 z^7 - 1797027375 z^8 + 1006335330 z^9 - 216514571 z^10))

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]
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