Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9np)

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=-19/4, b>=a

For fixed z and a=-19/4, b=13/4

http://functions.wolfram.com/07.23.03.a9np.01

Input Form

Hypergeometric2F1[-(19/4), 13/4, 9/2, z] == (1/(47586825 Pi^(3/2) z^(7/2))) (16 (-8 (43890 - 30723 z - 67298 z^2 - 487179 z^3 + 3018510 z^4 - 5807120 z^5 + 5384064 z^6 - 2482176 z^7 + 458752 z^8) EllipticE[(1/2) (1 - Sqrt[z])] + 8 (43890 - 30723 z - 67298 z^2 - 487179 z^3 + 3018510 z^4 - 5807120 z^5 + 5384064 z^6 - 2482176 z^7 + 458752 z^8) EllipticE[(1/2) (1 + Sqrt[z])] + (175560 + 87780 Sqrt[z] - 122892 z - 54131 z^(3/2) - 269192 z^2 - 136059 z^(5/2) - 1948716 z^3 + 1988415 z^(7/2) + 12074040 z^4 - 4624565 z^(9/2) - 23228480 z^5 + 4755840 z^(11/2) + 21536256 z^6 - 2353152 z^(13/2) - 9928704 z^7 + 458752 z^(15/2) + 1835008 z^8) EllipticK[(1/2) (1 - Sqrt[z])] - (175560 - 87780 Sqrt[z] - 122892 z + 54131 z^(3/2) - 269192 z^2 + 136059 z^(5/2) - 1948716 z^3 - 1988415 z^(7/2) + 12074040 z^4 + 4624565 z^(9/2) - 23228480 z^5 - 4755840 z^(11/2) + 21536256 z^6 + 2353152 z^(13/2) - 9928704 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'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 1835008 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 458752 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9928704 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2353152 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 21536256 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4755840 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> 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type='integer'> 4755840 </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'> 23228480 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4624565 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12074040 </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'> 1988415 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1948716 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <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]