Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.a7rg)

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=19/4

http://functions.wolfram.com/07.23.03.a7rg.01

Input Form

Hypergeometric2F1[-(23/4), 19/4, 6, z] == -((1/(1653098482035 Pi z^5)) (16384 Sqrt[1 + Sqrt[z]] ((-894976 + 433504 z + 753825 z^2 + 2006267 z^3 + 10385305 z^4 - 157878903 z^5 + 471469362 z^6 - 662117040 z^7 + 500344416 z^8 - 197733120 z^9 + 32248320 z^10) EllipticE[(2 Sqrt[z])/(1 + Sqrt[z])] + (894976 - 894976 Sqrt[z] + 237728 z - 237728 z^(3/2) - 470649 z^2 + 470649 z^(5/2) - 2292065 z^3 + 2292065 z^(7/2) - 12128935 z^4 + 12128935 z^(9/2) - 53283867 z^5 + 53283867 z^(11/2) + 393018444 z^6 - 393018444 z^(13/2) - 788338512 z^7 + 788338512 z^(15/2) + 745205760 z^8 - 745205760 z^(17/2) - 347093760 z^9 + 347093760 z^(19/2) + 64496640 z^10 - 64496640 z^(21/2)) EllipticK[(2 Sqrt[z])/(1 + Sqrt[z])])))

Standard Form

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MathML Form

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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]