Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b30z)

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=17/5, b>=a

For fixed z and a=17/5, b=5

http://functions.wolfram.com/07.23.03.b30z.01

Input Form

Hypergeometric2F1[17/5, 5, 27/5, z] == (1/93750) (187 (-(900/(-1 + z)^3) + 3570/z^4 + 1650/z^3 + 775/z^2 + 525/z + (800 z)/(-1 + z)^3 - (525 z^2)/(-1 + z)^3 + (84 (17 + 3 z) Log[1 - z^(1/5)])/z^(22/5) - (84 (-1)^(3/5) (17 + 3 z) Log[1 + (-1)^(1/5) z^(1/5)])/z^(22/5) - (1428 (-1)^(1/5) Log[1 - (-1)^(2/5) z^(1/5)])/z^(22/5) - (252 (-1)^(1/5) Log[1 - (-1)^(2/5) z^(1/5)])/z^(17/5) + (1428 (-1)^(4/5) Log[1 + (-1)^(3/5) z^(1/5)])/z^(22/5) + (252 (-1)^(4/5) Log[1 + (-1)^(3/5) z^(1/5)])/z^(17/5) + (1428 (-1)^(2/5) Log[1 - (-1)^(4/5) z^(1/5)])/z^(22/5) + (252 (-1)^(2/5) Log[1 - (-1)^(4/5) z^(1/5)])/z^(17/5)))

Standard Form

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MathML Form

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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> <power /> <apply> <power /> <ci> z </ci> <cn type='rational'> 22 <sep /> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1428 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <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 /> <apply> <power /> <ci> z </ci> <cn type='rational'> 22 <sep /> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1428 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <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'> 4 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='rational'> 22 <sep /> 5 </cn> </apply> <cn type='integer'> -1 </cn> </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]