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

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=-1/5, b>=a

For fixed z and a=-1/5, b=6

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

Input Form

Hypergeometric2F1[-(1/5), 6, 24/5, -z] == (1/(97656250 z^(19/5) (1 + z))) (399 (-1)^(1/5) (12 (-1)^(4/5) (-21 + 45 z - 110 z^2 + 440 z^3 + 4620 z^4 + 4004 z^5) Log[1 + z^(1/5)] + 12 (-21 + 45 z - 110 z^2 + 440 z^3 + 4620 z^4 + 4004 z^5) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(1/5) (12 (-21 + 45 z - 110 z^2 + 440 z^3 + 4620 z^4 + 4004 z^5) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (-12 (-21 + 45 z - 110 z^2 + 440 z^3 + 4620 z^4 + 4004 z^5) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (63 - 163 z + 408 z^2 + 47432 z^3 + 48048 z^4) + 12 (-21 + 45 z - 110 z^2 + 440 z^3 + 4620 z^4 + 4004 z^5) Log[1 + (-1)^(4/5) z^(1/5)])))))

Standard Form

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MathML Form

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</apply> <cn type='integer'> 63 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4004 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4620 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 440 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 110 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 45 </cn> <ci> z </ci> </apply> <cn type='integer'> -21 </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> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4004 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4620 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 440 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 110 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 45 </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'> 3 <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> </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]