Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab17)

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=-15/4, b>=a

For fixed z and a=-15/4, b=-15/4

http://functions.wolfram.com/07.23.03.ab17.01

Input Form

Hypergeometric2F1[-(15/4), -(15/4), 5, z] == (1/(17169326707995 Pi z^4)) (4096 (8 Sqrt[1 - z] (-36960 + 719180 z - 8028405 z^2 + 88455675 z^3 + 1613858198 z^4 + 2568166362 z^5 + 878398527 z^6 + 50446943 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] - 4 Sqrt[1 - z] (-36960 + 719180 z - 8028405 z^2 + 88455675 z^3 + 1613858198 z^4 + 2568166362 z^5 + 878398527 z^6 + 50446943 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])] + (147840 - 2987600 z + 34260765 z^2 - 377710410 z^3 + 2191226383 z^4 + 17647322196 z^5 + 17869391979 z^6 + 4033363942 z^7 + 140821065 z^8) 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]