Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a999)

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=-5/4

http://functions.wolfram.com/07.23.03.a999.01

Input Form

Hypergeometric2F1[-(19/4), -(5/4), 3, -z] == (1/(531485955 Pi z^2)) (64 (1 + z)^(1/4) (2 (-29260 - 636405 z + 25220064 z^2 - 32596062 z^3 + 341640 z^4 + 48555 z^5 + 3900 z^6) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + 4 Sqrt[1 + z] (7315 + 153615 z - 2267136 z^2 + 1389570 z^3 + 153855 z^4 + 22815 z^5 + 1950 z^6) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - (-29260 - 636405 z + 25220064 z^2 - 32596062 z^3 + 341640 z^4 + 48555 z^5 + 3900 z^6) EllipticK[1/2 - 1/(2 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]