Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aw0g)

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=-6/5, b>=a

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

http://functions.wolfram.com/07.23.03.aw0g.01

Input Form

Hypergeometric2F1[-(6/5), 6, 29/5, z] == (1/(6103515625 z^(24/5))) (798 (-1)^(1/5) (12 (-1)^(4/5) (399 + 756 z + 1485 z^2 + 3520 z^3 + 13860 z^4 - 144144 z^5 + 124124 z^6) Log[1 - z^(1/5)] + 12 (399 + 756 z + 1485 z^2 + 3520 z^3 + 13860 z^4 - 144144 z^5 + 124124 z^6) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(1/5) (-12 (399 + 756 z + 1485 z^2 + 3520 z^3 + 13860 z^4 - 144144 z^5 + 124124 z^6) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (12 (399 + 756 z + 1485 z^2 + 3520 z^3 + 13860 z^4 - 144144 z^5 + 124124 z^6) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (1197 + 2800 z + 5805 z^2 + 13440 z^3 - 1481480 z^4 + 1489488 z^5) - 12 (399 + 756 z + 1485 z^2 + 3520 z^3 + 13860 z^4 - 144144 z^5 + 124124 z^6) Log[1 - (-1)^(4/5) z^(1/5)])))))

Standard Form

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MathML Form

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12 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 124124 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 144144 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 13860 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3520 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1485 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 756 </cn> <ci> z </ci> </apply> <cn type='integer'> 399 </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> 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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]