Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aee1)

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=-9/4, b>=a

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

http://functions.wolfram.com/07.23.03.aee1.01

Input Form

Hypergeometric2F1[-(9/4), 9/4, 6, z] == (1/(777251475 Pi Sqrt[1 + Sqrt[z]] z^5)) (16384 ((18432 + 18432 Sqrt[z] - 88416 z - 88416 z^(3/2) + 152139 z^2 + 152139 z^(5/2) - 86625 z^3 - 86625 z^(7/2) - 38115 z^4 - 38115 z^(9/2) + 175021 z^5 + 175021 z^(11/2) - 117348 z^6 - 117348 z^(13/2) + 25872 z^7 + 25872 z^(15/2)) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] - (18432 - 93024 z + 172947 z^2 - 119145 z^3 - 24255 z^4 + 91861 z^5 - 59752 z^6 + 12936 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]