Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.abq3)

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.abq3.01

Input Form

Hypergeometric2F1[-(15/4), 17/4, 5, z] == (1/(5492021535 Pi z^4)) (4096 (-8 Sqrt[1 - z] (7392 + 8932 z + 15939 z^2 + 53823 z^3 - 973424 z^4 + 2072448 z^5 - 1646592 z^6 + 458752 z^7) EllipticE[(1/2) (1 - Sqrt[1 - z])] + (29568 + 13552 z + 34881 z^2 + 164010 z^3 - 1379723 z^4 + 2476416 z^5 - 1775616 z^6 + 458752 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])] + 4 Sqrt[1 - z] (7392 + 8932 z + 15939 z^2 + 53823 z^3 - 973424 z^4 + 2072448 z^5 - 1646592 z^6 + 458752 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])]))

Standard Form

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MathML Form

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type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2476416 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1379723 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 164010 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 34881 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 13552 </cn> <ci> z </ci> </apply> <cn type='integer'> 29568 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <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]