Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ab2t)

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=-13/4

http://functions.wolfram.com/07.23.03.ab2t.01

Input Form

Hypergeometric2F1[-(15/4), -(13/4), 6, z] == (1/(31588277195475 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((26624 - 475488 z + 4412135 z^2 - 30840810 z^3 + 233258025 z^4 + 5636732052 z^5 + 8424557001 z^6 + 2751032790 z^7 + 161166855 z^8) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (-26624 + 26624 Sqrt[z] + 455520 z - 455520 z^(3/2) - 4073615 z^2 + 4073615 z^(5/2) + 27837810 z^3 - 27837810 z^(7/2) - 212837625 z^4 + 212837625 z^(9/2) - 1937276292 z^5 + 1937276292 z^(11/2) - 1827837585 z^6 + 1827837585 z^(13/2) - 334960110 z^7 + 334960110 z^(15/2) - 6248775 z^8 + 6248775 z^(17/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[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]