Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9291)

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=-7/4

http://functions.wolfram.com/07.23.03.9291.01

Input Form

Hypergeometric2F1[-(23/4), -(7/4), 5/2, z] == (1/(93731625 Pi^(3/2) z^(3/2))) (4 (4 (100947 - 4744509 z - 61626946 z^2 - 80449490 z^3 - 4933305 z^4 + 753519 z^5 - 102648 z^6 + 7488 z^7) EllipticE[(1/2) (1 - Sqrt[z])] - 4 (100947 - 4744509 z - 61626946 z^2 - 80449490 z^3 - 4933305 z^4 + 753519 z^5 - 102648 z^6 + 7488 z^7) EllipticE[(1/2) (1 + Sqrt[z])] - (201894 + 100947 Sqrt[z] - 9489018 z - 28169003 z^(3/2) - 123253892 z^2 - 153406450 z^(5/2) - 160898980 z^3 - 120831750 z^(7/2) - 9866610 z^4 + 362895 z^(9/2) + 1507038 z^5 - 50271 z^(11/2) - 205296 z^6 + 3744 z^(13/2) + 14976 z^7) EllipticK[(1/2) (1 - Sqrt[z])] + (201894 - 100947 Sqrt[z] - 9489018 z + 28169003 z^(3/2) - 123253892 z^2 + 153406450 z^(5/2) - 160898980 z^3 + 120831750 z^(7/2) - 9866610 z^4 - 362895 z^(9/2) + 1507038 z^5 + 50271 z^(11/2) - 205296 z^6 - 3744 z^(13/2) + 14976 z^7) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

Standard Form

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MathML Form

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</cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9866610 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 120831750 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 160898980 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 153406450 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 123253892 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 28169003 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> 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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]