Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a92u)

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=-15/4

http://functions.wolfram.com/07.23.03.a92u.01

Input Form

Hypergeometric2F1[-(19/4), -(15/4), 4, z] == (1/(29149960455 Pi z^3)) (256 (2 Sqrt[1 - z] (12320 - 315315 z + 6077610 z^2 + 199651523 z^3 + 527739372 z^4 + 318999267 z^5 + 40644458 z^6 + 239085 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (12320 - 315315 z + 6077610 z^2 + 199651523 z^3 + 527739372 z^4 + 318999267 z^5 + 40644458 z^6 + 239085 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])] + (-12320 + 324555 z - 6313230 z^2 + 32618977 z^3 + 622311564 z^4 + 1068799581 z^5 + 433222018 z^6 + 35145495 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]