Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7sv)

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=21/4

http://functions.wolfram.com/07.23.03.a7sv.01

Input Form

Hypergeometric2F1[-(23/4), 21/4, 2, -z] == (8 Sqrt[2] (Sqrt[1 + z] (2187185 + 482340351 z + 5646460320 z^2 + 22246647808 z^3 + 38865469440 z^4 + 31180455936 z^5 + 9395240960 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (2187185 + 484527536 z + 6128800671 z^2 + 27893108128 z^3 + 61112117248 z^4 + 70045925376 z^5 + 40575696896 z^6 + 9395240960 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (2187185 + 233001261 z + 2204154072 z^2 + 7472227840 z^3 + 11605966848 z^4 + 8455716864 z^5 + 2348810240 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (2187185 + 482340351 z + 5646460320 z^2 + 22246647808 z^3 + 38865469440 z^4 + 31180455936 z^5 + 9395240960 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (1003917915 Pi z Sqrt[1 + Sqrt[1 + z]])

Standard Form

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MathML Form

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<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='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]