Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b1u5)

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=12/5, b>=a

For fixed z and a=12/5, b=6

http://functions.wolfram.com/07.23.03.b1u5.01

Input Form

Hypergeometric2F1[12/5, 6, 22/5, z] == (1/390625) (17 ((25 (859 - 472 z - 108 z^2 + 96 z^3))/(-1 + z)^4 - (1/z^(12/5)) (156 (35 z^(2/5) + 10 z^(7/5) + 14 Log[1 - z^(1/5)] - 14 (-1)^(3/5) Log[1 + (-1)^(1/5) z^(1/5)] - 14 (-1)^(1/5) Log[1 - (-1)^(2/5) z^(1/5)] + 14 (-1)^(4/5) Log[1 + (-1)^(3/5) z^(1/5)] + 14 (-1)^(2/5) Log[1 - (-1)^(4/5) z^(1/5)])) - (1/z^(17/5)) (24 (210 z^(2/5) + 60 z^(7/5) + 35 z^(12/5) + 84 Log[1 - z^(1/5)] - 84 (-1)^(3/5) Log[1 + (-1)^(1/5) z^(1/5)] - 84 (-1)^(1/5) Log[1 - (-1)^(2/5) z^(1/5)] + 84 (-1)^(4/5) Log[1 + (-1)^(3/5) z^(1/5)] + 84 (-1)^(2/5) Log[1 - (-1)^(4/5) z^(1/5)]))))

Standard Form

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MathML Form

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</apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 84 </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'> 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> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 84 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 5 </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'> 2 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </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]