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

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=-17/4, b>=a

For fixed z and a=-17/4, b=-5/4

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

Input Form

Hypergeometric2F1[-(17/4), -(5/4), 9/2, z] == (1/(17658961551 Pi^(3/2) z^(7/2))) (4 (2 Sqrt[z] (66300 - 951405 z + 7886385 z^2 + 1019726382 z^3 + 1049192814 z^4 + 41585775 z^5 - 3811115 z^6 + 234080 z^7) EllipticE[(1/2) (1 - Sqrt[z])] + 2 Sqrt[z] (66300 - 951405 z + 7886385 z^2 + 1019726382 z^3 + 1049192814 z^4 + 41585775 z^5 - 3811115 z^6 + 234080 z^7) EllipticE[(1/2) (1 + Sqrt[z])] - (-132600 + 66300 Sqrt[z] + 2002260 z - 951405 z^(3/2) - 17184960 z^2 + 7886385 z^(5/2) + 179540400 z^3 + 1019726382 z^(7/2) + 1211035416 z^4 + 1049192814 z^(9/2) + 739546500 z^5 + 41585775 z^(11/2) - 936320 z^6 - 3811115 z^(13/2) + 58520 z^7 + 234080 z^(15/2)) EllipticK[(1/2) (1 - Sqrt[z])] - (132600 + 66300 Sqrt[z] - 2002260 z - 951405 z^(3/2) + 17184960 z^2 + 7886385 z^(5/2) - 179540400 z^3 + 1019726382 z^(7/2) - 1211035416 z^4 + 1049192814 z^(9/2) - 739546500 z^5 + 41585775 z^(11/2) + 936320 z^6 - 3811115 z^(13/2) - 58520 z^7 + 234080 z^(15/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[1/4]^2)

Standard Form

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MathML Form

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</cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 951405 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 66300 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 234080 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 58520 </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'> 3811115 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times 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</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]