Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a933)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-19/4, b>=a

For fixed z and a=-19/4, b=-15/4

http://functions.wolfram.com/07.23.03.a933.01

Input Form

Hypergeometric2F1[-(19/4), -(15/4), 6, -z] == (16384 Sqrt[2] (Sqrt[1 + z] (-22528 - 467808 z - 5169857 z^2 - 44490677 z^3 - 434948745 z^4 + 7761695627 z^5 - 13555779643 z^6 + 5835969273 z^7 - 555859067 z^8 + 2470545 z^9) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-22528 - 490336 z - 5637665 z^2 - 49660534 z^3 - 479439422 z^4 + 7326746882 z^5 - 5794084016 z^6 - 7719810370 z^7 + 5280110206 z^8 - 553388522 z^9 + 2470545 z^10) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - Sqrt[1 + z] (-22528 - 467808 z - 5169857 z^2 - 44490677 z^3 - 434948745 z^4 + 7761695627 z^5 - 13555779643 z^6 + 5835969273 z^7 - 555859067 z^8 + 2470545 z^9) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (22528 + 484704 z + 5519129 z^2 + 48335903 z^3 + 467967885 z^4 + 2599636123 z^5 - 21467936021 z^6 + 24772751709 z^7 - 7341227857 z^8 + 457050825 z^9) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (82232038443555 Pi z^5 Sqrt[1 + Sqrt[1 + z]])

Standard Form

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MathML Form

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type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 44490677 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5169857 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 467808 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -22528 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> 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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]