Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9ab)

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=-3/4

http://functions.wolfram.com/07.23.03.a9ab.01

Input Form

Hypergeometric2F1[-(19/4), -(3/4), 7/2, z] == (1/(131224275 Pi^(3/2) z^(5/2))) (8 (2 (-52668 + 820743 z - 11534292 z^2 - 44101190 z^3 - 4675320 z^4 + 976599 z^5 - 169104 z^6 + 14976 z^7) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (-52668 + 820743 z - 11534292 z^2 - 44101190 z^3 - 4675320 z^4 + 976599 z^5 - 169104 z^6 + 14976 z^7) EllipticE[(1/2) (1 + Sqrt[z])] - (-52668 - 26334 Sqrt[z] + 820743 z + 408177 z^(3/2) - 11534292 z^2 - 22137080 z^(5/2) - 44101190 z^3 - 37160370 z^(7/2) - 4675320 z^4 + 232830 z^(9/2) + 976599 z^5 - 41223 z^(11/2) - 169104 z^6 + 3744 z^(13/2) + 14976 z^7) EllipticK[(1/2) (1 - Sqrt[z])] + (-52668 + 26334 Sqrt[z] + 820743 z - 408177 z^(3/2) - 11534292 z^2 + 22137080 z^(5/2) - 44101190 z^3 + 37160370 z^(7/2) - 4675320 z^4 - 232830 z^(9/2) + 976599 z^5 + 41223 z^(11/2) - 169104 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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type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 14976 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3744 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 169104 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 41223 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 976599 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </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]