Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.7586)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 3 and fixed z

For fixed z and a=1/3, b>=a

For fixed z and a=1/3, b=17/3

http://functions.wolfram.com/07.23.03.7586.01

Input Form

Hypergeometric2F1[1/3, 17/3, -(11/2), -z] == ((221709312 + 2638116864 z + 14478428160 z^2 + 48729423872 z^3 + 113447033856 z^4 + 199908988928 z^5 + 342329675776 z^6 + 54888640605 z^7 + 21661708108 z^8 + 6252506024 z^9 + 1126643040 z^10 + 94340480 z^11) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[z] Sqrt[1 + z] (-73903104 - 827366400 z - 4249598976 z^2 - 13313475584 z^3 - 28744151040 z^4 - 47290710016 z^5 + 46076196585 z^6 + 18928464836 z^7 + 5724562184 z^8 + 1079472800 z^9 + 94340480 z^10) Sinh[ArcSinh[Sqrt[z]]/3])/(221709312 (1 + z)^(23/2))

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]