Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9725)

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=-23/4, b>=a

For fixed z and a=-23/4, b=9/4

http://functions.wolfram.com/07.23.03.9725.01

Input Form

Hypergeometric2F1[-(23/4), 9/4, 3, -z] == (64 Sqrt[2] (2 Sqrt[1 + z] (-67298 + 168245 z + 3318912 z^2 + 10595225 z^3 + 15838816 z^4 + 12715776 z^5 + 5324800 z^6 + 917504 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 2 (-67298 + 100947 z + 3487157 z^2 + 13914137 z^3 + 26434041 z^4 + 28554592 z^5 + 18040576 z^6 + 6242304 z^7 + 917504 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-134596 + 235543 z + 2498997 z^2 + 6887941 z^3 + 9400043 z^4 + 7047552 z^5 + 2791424 z^6 + 458752 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 Sqrt[1 + z] (-67298 + 168245 z + 3318912 z^2 + 10595225 z^3 + 15838816 z^4 + 12715776 z^5 + 5324800 z^6 + 917504 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (140821065 Pi z^2 Sqrt[1 + Sqrt[1 + z]])

Standard Form

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MathML Form

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/> <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='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]