Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9390)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-23/4, b>=a

For fixed z and a=-23/4, b=-3/4

http://functions.wolfram.com/07.23.03.9390.01

Input Form

Hypergeometric2F1[-(23/4), -(3/4), 5, z] == (1/(64073584575 Pi z^4)) (4096 (2 Sqrt[1 - z] (-2944 + 43792 z - 348519 z^2 + 2457343 z^3 + 18313498 z^4 + 4003566 z^5 - 862883 z^6 + 183571 z^7 - 27552 z^8 + 2048 z^9) EllipticE[(1/2) (1 - Sqrt[1 - z])] - 4 (-736 + 11500 z - 95289 z^2 + 678937 z^3 - 3698072 z^4 - 8730666 z^5 - 56945 z^6 + 11941 z^7 - 1758 z^8 + 128 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (-2944 + 43792 z - 348519 z^2 + 2457343 z^3 + 18313498 z^4 + 4003566 z^5 - 862883 z^6 + 183571 z^7 - 27552 z^8 + 2048 z^9) EllipticK[(1/2) (1 - 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]