Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aao4)

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=-17/4, b>=a

For fixed z and a=-17/4, b=9/4

http://functions.wolfram.com/07.23.03.aao4.01

Input Form

Hypergeometric2F1[-(17/4), 9/4, 4, z] == (1/(50470875 Pi Sqrt[1 + Sqrt[z]] z^3)) (256 ((21216 + 21216 Sqrt[z] - 53703 z - 53703 z^(3/2) - 53703 z^2 - 53703 z^(5/2) + 850075 z^3 + 850075 z^(7/2) - 1725045 z^4 - 1725045 z^(9/2) + 1597848 z^5 + 1597848 z^(11/2) - 728784 z^6 - 728784 z^(13/2) + 133056 z^7 + 133056 z^(15/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (21216 - 59007 z - 41769 z^2 + 472165 z^3 - 915715 z^4 + 826518 z^5 - 369936 z^6 + 66528 z^7) 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]