Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9082)

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=-23/4, b>=a

For fixed z and a=-23/4, b=-17/4

http://functions.wolfram.com/07.23.03.9082.01

Input Form

Hypergeometric2F1[-(23/4), -(17/4), 3, z] == (1/(466821830475 Pi z^2)) (64 Sqrt[1 + Sqrt[z]] ((-4249388 + 205032971 z + 26322178170 z^2 + 165007123965 z^3 + 253751268720 z^4 + 110693649141 z^5 + 10957016418 z^6 + 3663075 z^7) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - 2 (-2124694 + 2124694 Sqrt[z] + 100922965 z - 100922965 z^(3/2) + 5942441220 z^2 - 5942441220 z^(5/2) + 27099795315 z^3 - 27099795315 z^(7/2) + 29397198570 z^4 - 29397198570 z^(9/2) + 8010039483 z^5 - 8010039483 z^(11/2) + 322350600 z^6 - 322350600 z^(13/2) - 3663075 z^7 + 3663075 z^(15/2)) 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]