Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.b2qz)

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=16/5, b>=a

For fixed z and a=16/5, b=4

http://functions.wolfram.com/07.23.03.b2qz.01

Input Form

Hypergeometric2F1[16/5, 4, 26/5, z] == (1/3125) (56 (-(175/(-1 + z)^2) - 5280/z^4 - 550/z^3 - 425/z^2 - 300/z + (300 z)/(-1 + z)^2 + (66 (-16 + z) Log[1 - z^(1/5)])/z^(21/5) + (66 (-1)^(4/5) (-16 + z) Log[1 + (-1)^(1/5) z^(1/5)])/z^(21/5) + (1056 (-1)^(3/5) Log[1 - (-1)^(2/5) z^(1/5)])/z^(21/5) - (66 (-1)^(3/5) Log[1 - (-1)^(2/5) z^(1/5)])/z^(16/5) - (1056 (-1)^(2/5) Log[1 + (-1)^(3/5) z^(1/5)])/z^(21/5) + (66 (-1)^(2/5) Log[1 + (-1)^(3/5) z^(1/5)])/z^(16/5) + (1056 (-1)^(1/5) Log[1 - (-1)^(4/5) z^(1/5)])/z^(21/5) - (66 (-1)^(1/5) Log[1 - (-1)^(4/5) z^(1/5)])/z^(16/5)))

Standard Form

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MathML Form

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</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'> 21 <sep /> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1056 </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'> 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'> 21 <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]