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

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=-11/4, b>=a

For fixed z and a=-11/4, b=21/4

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

Input Form

Hypergeometric2F1[-(11/4), 21/4, 11/2, z] == (1/(106229175 Pi^(3/2) z^(9/2))) (32 (-2 (-25872 - 43428 z - 94633 z^2 - 296835 z^3 - 2291520 z^4 + 11915776 z^5 - 14647296 z^6 + 5505024 z^7) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (-25872 - 43428 z - 94633 z^2 - 296835 z^3 - 2291520 z^4 + 11915776 z^5 - 14647296 z^6 + 5505024 z^7) EllipticE[(1/2) (1 + Sqrt[z])] + (-25872 - 12936 Sqrt[z] - 43428 z - 22792 z^(3/2) - 94633 z^2 - 49665 z^(5/2) - 296835 z^3 - 153615 z^(7/2) - 2291520 z^4 + 2158720 z^(9/2) + 11915776 z^5 - 3274752 z^(11/2) - 14647296 z^6 + 1376256 z^(13/2) + 5505024 z^7) EllipticK[(1/2) (1 - Sqrt[z])] - (-25872 + 12936 Sqrt[z] - 43428 z + 22792 z^(3/2) - 94633 z^2 + 49665 z^(5/2) - 296835 z^3 + 153615 z^(7/2) - 2291520 z^4 - 2158720 z^(9/2) + 11915776 z^5 + 3274752 z^(11/2) - 14647296 z^6 - 1376256 z^(13/2) + 5505024 z^7) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

Standard Form

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MathML Form

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type='integer'> 5505024 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1376256 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 14647296 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3274752 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11915776 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2158720 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 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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]