Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.abq6)

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=-15/4, b>=a

For fixed z and a=-15/4, b=17/4

http://functions.wolfram.com/07.23.03.abq6.01

Input Form

Hypergeometric2F1[-(15/4), 17/4, 11/2, z] == (1/(68736525 Pi^(3/2) z^(9/2))) (32 (2 (-129360 + 60060 z + 84007 z^2 + 211134 z^3 + 1484175 z^4 - 8000960 z^5 + 12142080 z^6 - 7766016 z^7 + 1835008 z^8) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (-129360 + 60060 z + 84007 z^2 + 211134 z^3 + 1484175 z^4 - 8000960 z^5 + 12142080 z^6 - 7766016 z^7 + 1835008 z^8) EllipticE[(1/2) (1 + Sqrt[z])] - (-129360 - 64680 Sqrt[z] + 60060 z + 24640 z^(3/2) + 84007 z^2 + 41811 z^(5/2) + 211134 z^3 + 108570 z^(7/2) + 1484175 z^4 - 1395845 z^(9/2) - 8000960 z^5 + 2559360 z^(11/2) + 12142080 z^6 - 1812480 z^(13/2) - 7766016 z^7 + 458752 z^(15/2) + 1835008 z^8) EllipticK[(1/2) (1 - Sqrt[z])] + (-129360 + 64680 Sqrt[z] + 60060 z - 24640 z^(3/2) + 84007 z^2 - 41811 z^(5/2) + 211134 z^3 - 108570 z^(7/2) + 1484175 z^4 + 1395845 z^(9/2) - 8000960 z^5 - 2559360 z^(11/2) + 12142080 z^6 + 1812480 z^(13/2) - 7766016 z^7 - 458752 z^(15/2) + 1835008 z^8) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

Standard Form

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MathML Form

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type='integer'> 7766016 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1812480 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12142080 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2559360 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8000960 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1395845 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1484175 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 108570 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 211134 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 41811 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 84007 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 24640 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 60060 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 64680 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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]