Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9021)

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=-19/4

http://functions.wolfram.com/07.23.03.9021.01

Input Form

Hypergeometric2F1[-(23/4), -(19/4), -(3/2), z] == (1/(7020 Pi^(3/2))) ((-2 Sqrt[z] (-3510 + 62595 z + 17345424 z^2 + 32637786 z^3 + 8612126 z^4 + 65835 z^5) EllipticE[(1/2) (1 - Sqrt[z])] + 2 Sqrt[z] (-3510 + 62595 z + 17345424 z^2 + 32637786 z^3 + 8612126 z^4 + 65835 z^5) EllipticE[(1/2) (1 + Sqrt[z])] + (7020 - 3510 Sqrt[z] - 130455 z + 62595 z^(3/2) + 2323620 z^2 + 17345424 z^(5/2) + 24050022 z^3 + 32637786 z^(7/2) + 27532424 z^4 + 8612126 z^(9/2) + 4937625 z^5 + 65835 z^(11/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (7020 + 3510 Sqrt[z] - 130455 z - 62595 z^(3/2) + 2323620 z^2 - 17345424 z^(5/2) + 24050022 z^3 - 32637786 z^(7/2) + 27532424 z^4 - 8612126 z^(9/2) + 4937625 z^5 - 65835 z^(11/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

Standard Form

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MathML Form

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<plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]