Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9982)

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=17/4

http://functions.wolfram.com/07.23.03.9982.01

Input Form

Hypergeometric2F1[-(23/4), 17/4, 3, z] == (1/(16476064605 Pi z^2)) (64 (-8 Sqrt[1 - z] (168245 + 3028410 z - 222623406 z^2 + 1381264493 z^3 - 3370240512 z^4 + 3999356928 z^5 - 2319450112 z^6 + 528482304 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] + (672980 + 11608905 z - 384749154 z^2 + 1965772565 z^3 - 4237170240 z^4 + 4583577600 z^5 - 2468085760 z^6 + 528482304 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])] + 4 Sqrt[1 - z] (168245 + 3028410 z - 222623406 z^2 + 1381264493 z^3 - 3370240512 z^4 + 3999356928 z^5 - 2319450112 z^6 + 528482304 z^7) 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]