Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b5cs)

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=21/8

http://functions.wolfram.com/07.23.03.b5cs.01

Input Form

Hypergeometric2F1[-(47/8), 21/8, 9/2, z] == (1/(27177092415 z^(7/2))) (128 ((1 + Sqrt[z])^(31/4) (-2144704 + 16621456 Sqrt[z] - 65681560 z + 181797175 z^(3/2) - 394089360 z^2 + 698101152 z^(5/2) - 990853248 z^3 + 1062969600 z^(7/2) - 806615040 z^4 + 402124800 z^(9/2) - 117325824 z^5 + 15138816 z^(11/2)) + (1 - Sqrt[z])^(31/4) (2144704 + 16621456 Sqrt[z] + 65681560 z + 181797175 z^(3/2) + 394089360 z^2 + 698101152 z^(5/2) + 990853248 z^3 + 1062969600 z^(7/2) + 806615040 z^4 + 402124800 z^(9/2) + 117325824 z^5 + 15138816 z^(11/2))))

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]