Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4630)

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=-17/3, b>=a

For fixed z and a=-17/3, b=-7/3

http://functions.wolfram.com/07.23.03.4630.01

Input Form

Hypergeometric2F1[-(17/3), -(7/3), 9/2, -z] == -((243 (Sqrt[z] (1769472 + 38469632 z + 511049728 z^2 - 55078839475 z^3 + 76844091907 z^4 + 76919920238 z^5 - 54746755592 z^6 + 782428352 z^7 + 54213760 z^8 + 2390528 z^9) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[1 + z] (-5308416 - 113836032 z - 1500119040 z^2 - 27441627136 z^3 + 258987729297 z^4 - 354345701754 z^5 + 94967389192 z^6 + 756217920 z^7 + 53018496 z^8 + 2390528 z^9) Sinh[ArcSinh[Sqrt[z]]/3]))/ (15641751950825 z^(7/2) Sqrt[1 + 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]