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

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=-11/5, b>=a

For fixed z and a=-11/5, b=6

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

Input Form

Hypergeometric2F1[-(11/5), 6, 19/5, z] == -((1/(2441406250 z^(14/5))) (21 (-1)^(1/5) (132 (-1)^(4/5) (-99 - 880 z - 9240 z^2 + 240240 z^3 - 620620 z^4 + 406224 z^5) Log[1 - z^(1/5)] + 132 (-99 - 880 z - 9240 z^2 + 240240 z^3 - 620620 z^4 + 406224 z^5) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(1/5) (-132 (-99 - 880 z - 9240 z^2 + 240240 z^3 - 620620 z^4 + 406224 z^5) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (132 (-99 - 880 z - 9240 z^2 + 240240 z^3 - 620620 z^4 + 406224 z^5) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (-3267 - 30492 z + 22932728 z^2 - 72984912 z^3 + 53621568 z^4) - 132 (-99 - 880 z - 9240 z^2 + 240240 z^3 - 620620 z^4 + 406224 z^5) Log[1 - (-1)^(4/5) z^(1/5)]))))))

Standard Form

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MathML Form

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</apply> </apply> <apply> <times /> <cn type='integer'> 22932728 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 30492 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -3267 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 132 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 406224 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 620620 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 240240 </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'> 9240 </cn> <apply> <power /> <ci> z 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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]