Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9471)

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=1/4

http://functions.wolfram.com/07.23.03.9471.01

Input Form

Hypergeometric2F1[-(23/4), 1/4, 2, -z] == (8 Sqrt[2] (Sqrt[1 + z] (-168245 + 1729557 z + 1926405 z^2 + 1659911 z^3 + 924300 z^4 + 294912 z^5 + 40960 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-168245 + 1561312 z + 3655962 z^2 + 3586316 z^3 + 2584211 z^4 + 1219212 z^5 + 335872 z^6 + 40960 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-168245 - 1803588 z + 573714 z^2 + 471260 z^3 + 250491 z^4 + 76608 z^5 + 10240 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-168245 + 1729557 z + 1926405 z^2 + 1659911 z^3 + 924300 z^4 + 294912 z^5 + 40960 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (13627845 Pi z Sqrt[1 + Sqrt[1 + z]])

Standard Form

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MathML Form

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type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </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]