Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a9re)

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=17/4

http://functions.wolfram.com/07.23.03.a9re.01

Input Form

Hypergeometric2F1[-(19/4), 17/4, 5, z] == (1/(27460107675 Pi z^4)) (4096 (2 Sqrt[1 - z] (-80256 - 103664 z - 209209 z^2 - 851466 z^3 + 20319715 z^4 - 58141312 z^5 + 69568512 z^6 - 38862848 z^7 + 8388608 z^8) EllipticE[(1/2) (1 - Sqrt[1 - z])] - 2 (-40128 - 21736 z - 62909 z^2 - 342342 z^3 + 3784835 z^4 - 9168776 z^5 + 9927168 z^6 - 5152768 z^7 + 1048576 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (-80256 - 103664 z - 209209 z^2 - 851466 z^3 + 20319715 z^4 - 58141312 z^5 + 69568512 z^6 - 38862848 z^7 + 8388608 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])]))

Standard Form

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MathML Form

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<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 type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 1048576 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5152768 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9927168 </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'> 9168776 </cn> <apply> <power /> <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]