Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.au95)

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=-11/5, b>=a

For fixed z and a=-11/5, b=4

http://functions.wolfram.com/07.23.03.au95.01

Input Form

Hypergeometric2F1[-(11/5), 4, 24/5, z] == -((1/(48828125 z^(19/5))) (133 (-1)^(1/5) (132 (-1)^(4/5) (-1 + z)^3 (21 + 72 z + 168 z^2 + 364 z^3) Log[1 - z^(1/5)] + 132 (-1 + z)^3 (21 + 72 z + 168 z^2 + 364 z^3) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(1/5) (-132 (-1 + z)^3 (21 + 72 z + 168 z^2 + 364 z^3) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (132 (-1 + z)^3 (21 + 72 z + 168 z^2 + 364 z^3) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (-693 - 605 z - 825 z^2 + 71160 z^3 - 113960 z^4 + 48048 z^5) - 132 (-1 + z)^3 (21 + 72 z + 168 z^2 + 364 z^3) Log[1 - (-1)^(4/5) z^(1/5)]))))))

Standard Form

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MathML Form

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<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> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 132 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 364 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 168 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 72 </cn> <ci> z </ci> </apply> <cn type='integer'> 21 </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> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]