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

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=-17/4, b>=a

For fixed z and a=-17/4, b=-1/4

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

Input Form

Hypergeometric2F1[-(17/4), -(1/4), 6, z] == (1/(86274913725 Pi z^5)) (16384 (-2 (-2048 + 24736 z - 143795 z^2 + 562099 z^3 - 1973582 z^4 - 19870778 z^5 - 1269919 z^6 + 233975 z^7 - 35056 z^8 + 2688 z^9) EllipticE[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (2048 - 24224 z + 137979 z^2 - 530293 z^3 + 1855510 z^4 + 9749838 z^5 + 52591 z^6 - 8281 z^7 + 672 z^8) EllipticK[(1/2) (1 - Sqrt[1 - z])] + (-2048 + 24736 z - 143795 z^2 + 562099 z^3 - 1973582 z^4 - 19870778 z^5 - 1269919 z^6 + 233975 z^7 - 35056 z^8 + 2688 z^9) EllipticK[(1/2) (1 - Sqrt[1 - z])]))

Standard Form

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MathML Form

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type='rational'> 17 <sep /> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </list> <list> <cn type='integer'> 6 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 86274913725 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 16384 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2688 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 35056 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 233975 </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]