Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9853)

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=13/4

http://functions.wolfram.com/07.23.03.9853.01

Input Form

Hypergeometric2F1[-(23/4), 13/4, 3, -z] == (64 Sqrt[2] (Sqrt[1 + z] (-134596 + 1379609 z + 65191554 z^2 + 304240693 z^3 + 595603840 z^4 + 590395392 z^5 + 294060032 z^6 + 58720256 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-134596 + 1245013 z + 66571163 z^2 + 369432247 z^3 + 899844533 z^4 + 1185999232 z^5 + 884455424 z^6 + 352780288 z^7 + 58720256 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 (-67298 + 639331 z + 13314900 z^2 + 51922871 z^3 + 91039160 z^4 + 83191296 z^5 + 38821888 z^6 + 7340032 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-134596 + 1379609 z + 65191554 z^2 + 304240693 z^3 + 595603840 z^4 + 590395392 z^5 + 294060032 z^6 + 58720256 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (1267389585 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]