Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a90f)

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=-19/4

http://functions.wolfram.com/07.23.03.a90f.01

Input Form

Hypergeometric2F1[-(19/4), -(19/4), 7/2, z] == (1/(323467837875 Pi^(3/2) z^(5/2))) (8 (-2 (11007612 - 384349119 z + 15019886574 z^2 + 258505264535 z^3 + 731138839120 z^4 + 569994295359 z^5 + 121764017062 z^6 + 4758088073 z^7) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (11007612 - 384349119 z + 15019886574 z^2 + 258505264535 z^3 + 731138839120 z^4 + 569994295359 z^5 + 121764017062 z^6 + 4758088073 z^7) EllipticE[(1/2) (1 + Sqrt[z])] + (11007612 + 5503806 Sqrt[z] - 384349119 z - 191715909 z^(3/2) + 15019886574 z^2 + 47927637800 z^(5/2) + 258505264535 z^3 + 385467956425 z^(7/2) + 731138839120 z^4 + 749334272310 z^(9/2) + 569994295359 z^5 + 442707561997 z^(11/2) + 121764017062 z^6 + 73446150212 z^(13/2) + 4758088073 z^7 + 2109682575 z^(15/2)) EllipticK[(1/2) (1 - Sqrt[z])] + (-11007612 + 5503806 Sqrt[z] + 384349119 z - 191715909 z^(3/2) - 15019886574 z^2 + 47927637800 z^(5/2) - 258505264535 z^3 + 385467956425 z^(7/2) - 731138839120 z^4 + 749334272310 z^(9/2) - 569994295359 z^5 + 442707561997 z^(11/2) - 121764017062 z^6 + 73446150212 z^(13/2) - 4758088073 z^7 + 2109682575 z^(15/2)) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

Standard Form

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MathML Form

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<ci> z </ci> </apply> </apply> <cn type='integer'> 11007612 </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 /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2109682575 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4758088073 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 73446150212 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 121764017062 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 442707561997 </cn> <apply> <power /> <ci> z </ci> 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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]