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

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=-7/4, b>=a

For fixed z and a=-7/4, b=21/4

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

Input Form

Hypergeometric2F1[-(7/4), 21/4, 7/2, z] == (1/(2197845 Pi^(3/2) z^(5/2))) (8 (2 (1764 + 13965 z + 169344 z^2 - 1034240 z^3 + 983040 z^4) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (1764 + 13965 z + 169344 z^2 - 1034240 z^3 + 983040 z^4) EllipticE[(1/2) (1 + Sqrt[z])] - (1764 + 882 Sqrt[z] + 13965 z + 7056 z^(3/2) + 169344 z^2 - 189440 z^(5/2) - 1034240 z^3 + 245760 z^(7/2) + 983040 z^4) EllipticK[(1/2) (1 - Sqrt[z])] + (1764 - 882 Sqrt[z] + 13965 z - 7056 z^(3/2) + 169344 z^2 + 189440 z^(5/2) - 1034240 z^3 - 245760 z^(7/2) + 983040 z^4) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

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]