Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9nq)

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=-19/4, b>=a

For fixed z and a=-19/4, b=13/4

http://functions.wolfram.com/07.23.03.a9nq.01

Input Form

Hypergeometric2F1[-(19/4), 13/4, 5, z] == (1/(2112315975 Pi z^4)) (4096 (4 Sqrt[1 - z] (13376 - 21736 z - 24871 z^2 - 55594 z^3 + 726665 z^4 - 1559968 z^5 + 1503488 z^6 - 704512 z^7 + 131072 z^8) EllipticE[(1/2) (1 - Sqrt[1 - z])] - (26752 - 63536 z - 19019 z^2 - 71687 z^3 + 509695 z^4 - 951101 z^5 + 842368 z^6 - 370688 z^7 + 65536 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])] - 2 Sqrt[1 - z] (13376 - 21736 z - 24871 z^2 - 55594 z^3 + 726665 z^4 - 1559968 z^5 + 1503488 z^6 - 704512 z^7 + 131072 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]