Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.ap9o)

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=-26/5, b>=a

For fixed z and a=-26/5, b=4

http://functions.wolfram.com/07.23.03.ap9o.01

Input Form

Hypergeometric2F1[-(26/5), 4, 29/5, z] == (1/(152587890625 z^(24/5))) (19 (-1)^(1/5) (144144 (-1)^(4/5) (-1 + z)^7 (133 + 651 z + 1674 z^2 + 2542 z^3) Log[1 - z^(1/5)] + 144144 (-1 + z)^7 (133 + 651 z + 1674 z^2 + 2542 z^3) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(1/5) (-144144 (-1 + z)^7 (133 + 651 z + 1674 z^2 + 2542 z^3) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (144144 (-1 + z)^7 (133 + 651 z + 1674 z^2 + 2542 z^3) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (-4792788 + 7959952 z + 6358352 z^2 + 9081072 z^3 - 1573625973 z^4 + 5243050488 z^5 - 7566706602 z^6 + 5745496848 z^7 - 2262532272 z^8 + 366414048 z^9) - 144144 (-1 + z)^7 (133 + 651 z + 1674 z^2 + 2542 z^3) Log[1 - (-1)^(4/5) z^(1/5)])))))

Standard Form

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MathML Form

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3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6358352 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7959952 </cn> <ci> z </ci> </apply> <cn type='integer'> -4792788 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 144144 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 7 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2542 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1674 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 651 </cn> <ci> z </ci> </apply> <cn type='integer'> 133 </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> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 144144 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 7 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2542 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1674 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 651 </cn> <ci> z </ci> </apply> <cn type='integer'> 133 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> 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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]