Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.apm2)

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=-24/5, b>=a

For fixed z and a=-24/5, b=3

http://functions.wolfram.com/07.23.03.apm2.01

Input Form

Hypergeometric2F1[-(24/5), 3, -(9/5), -z] == (1/9375) (9375 - 75000 z + 712500 z^2 + 5708360 z^3 + 5901210 z^4 + 9576 z^(14/5) (228 + 696 z + 493 z^2) Log[1 + z^(1/5)] + 9576 (-1)^(4/5) z^(14/5) (228 + 696 z + 493 z^2) Log[1 - (-1)^(1/5) z^(1/5)] - 2183328 (-1)^(3/5) z^(14/5) Log[1 + (-1)^(2/5) z^(1/5)] - 6664896 (-1)^(3/5) z^(19/5) Log[1 + (-1)^(2/5) z^(1/5)] - 4720968 (-1)^(3/5) z^(24/5) Log[1 + (-1)^(2/5) z^(1/5)] + 2183328 (-1)^(2/5) z^(14/5) Log[1 - (-1)^(3/5) z^(1/5)] + 6664896 (-1)^(2/5) z^(19/5) Log[1 - (-1)^(3/5) z^(1/5)] + 4720968 (-1)^(2/5) z^(24/5) Log[1 - (-1)^(3/5) z^(1/5)] - 2183328 (-1)^(1/5) z^(14/5) Log[1 + (-1)^(4/5) z^(1/5)] - 6664896 (-1)^(1/5) z^(19/5) Log[1 + (-1)^(4/5) z^(1/5)] - 4720968 (-1)^(1/5) z^(24/5) Log[1 + (-1)^(4/5) z^(1/5)])

Standard Form

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MathML Form

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type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <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> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 24 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5901210 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6664896 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> 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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> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 19 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5708360 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9576 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 493 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 696 </cn> <ci> z </ci> </apply> <cn type='integer'> 228 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 14 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9576 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 493 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 696 </cn> <ci> z </ci> </apply> <cn type='integer'> 228 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <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> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 14 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2183328 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <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]