Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.8035)

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=4/3, b>=a

For fixed z and a=4/3, b=17/3

http://functions.wolfram.com/07.23.03.8035.01

Input Form

Hypergeometric2F1[4/3, 17/3, -(7/2), -z] == (1/(3483648 (1 + z)^(21/2))) ((3483648 + 44292096 z + 278493184 z^2 + 1260464128 z^3 + 7107358720 z^4 - 14459833751 z^5 - 561688704 z^6 - 118016312 z^7 - 18505248 z^8 - 1451392 z^9) Cosh[ArcSinh[Sqrt[z]]/3] - Sqrt[z] Sqrt[1 + z] (1161216 + 13946880 z + 83105792 z^2 + 362700800 z^3 - 5985994949 z^4 + 509166456 z^5 + 109307960 z^6 + 17779552 z^7 + 1451392 z^8) Sinh[ArcSinh[Sqrt[z]]/3])

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]