Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a87d)

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=-21/4, b>=a

For fixed z and a=-21/4, b=-17/4

http://functions.wolfram.com/07.23.03.a87d.01

Input Form

Hypergeometric2F1[-(21/4), -(17/4), 4, z] == (1/(80501045625 Pi z^3)) (256 (2 (21216 - 633165 z + 14336049 z^2 + 1562478475 z^3 + 7280035825 z^4 + 8632594561 z^5 + 2954273115 z^6 + 230358849 z^7 + 480675 z^8) EllipticE[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (21216 - 627861 z + 14181570 z^2 + 937037425 z^3 + 3889827500 z^4 + 4151633181 z^5 + 1261742994 z^6 + 83156775 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])] - (21216 - 633165 z + 14336049 z^2 + 1562478475 z^3 + 7280035825 z^4 + 8632594561 z^5 + 2954273115 z^6 + 230358849 z^7 + 480675 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]