Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.any1)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 5 and fixed z

For fixed z and a=-29/5, b>=a

For fixed z and a=-29/5, b=2

http://functions.wolfram.com/07.23.03.any1.01

Input Form

Hypergeometric2F1[-(29/5), 2, -(14/5), z] == (1/13125) (13125 + 54375 z + 217500 z^2 + 1377500 z^3 - 7444010 z^4 + 5901210 z^5 + 277704 z^(19/5) (12 - 29 z + 17 z^2) Log[1 - z^(1/5)] + 277704 (-1)^(4/5) z^(19/5) (12 - 29 z + 17 z^2) Log[1 + (-1)^(1/5) z^(1/5)] - 3332448 (-1)^(3/5) z^(19/5) Log[1 - (-1)^(2/5) z^(1/5)] + 8053416 (-1)^(3/5) z^(24/5) Log[1 - (-1)^(2/5) z^(1/5)] - 4720968 (-1)^(3/5) z^(29/5) Log[1 - (-1)^(2/5) z^(1/5)] + 3332448 (-1)^(2/5) z^(19/5) Log[1 + (-1)^(3/5) z^(1/5)] - 8053416 (-1)^(2/5) z^(24/5) Log[1 + (-1)^(3/5) z^(1/5)] + 4720968 (-1)^(2/5) z^(29/5) Log[1 + (-1)^(3/5) z^(1/5)] - 3332448 (-1)^(1/5) z^(19/5) Log[1 - (-1)^(4/5) z^(1/5)] + 8053416 (-1)^(1/5) z^(24/5) Log[1 - (-1)^(4/5) z^(1/5)] - 4720968 (-1)^(1/5) z^(29/5) Log[1 - (-1)^(4/5) z^(1/5)])

Standard Form

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MathML Form

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type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 24 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7444010 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 277704 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 17 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 29 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 12 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 19 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 277704 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 17 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 29 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 12 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 19 <sep /> 5 </cn> </apply> 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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]