Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b96x)

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=-41/8, b>=a

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

http://functions.wolfram.com/07.23.03.b96x.01

Input Form

Hypergeometric2F1[-(41/8), 19/8, 11/4, z] == (2 2^(3/4) (-31365 + 5804515 z - 24241495 z^2 + 42787353 z^3 - 38839584 z^4 + 17939712 z^5 - 3354624 z^6 + (1/Sqrt[1 - z]) (31365 + 6159985 z - 34122465 z^2 + 79694043 z^3 - 100563568 z^4 + 72067968 z^5 - 27740160 z^6 + 4472832 z^7)))/ (23960365 (1 + Sqrt[1 - z])^(3/4) 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]