Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4696)

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=2/3

http://functions.wolfram.com/07.23.03.4696.01

Input Form

Hypergeometric2F1[-(17/3), 2/3, 3/2, -z] == (1/1416545) (3 ((1/Sqrt[1 + z]) ((344523 + 1144195 z + 1853552 z^2 + 1845016 z^3 + 1108960 z^4 + 371072 z^5 + 53248 z^6) Cosh[ArcSinh[Sqrt[z]]/3]) + (1/Sqrt[z]) ((382976 + 651111 z + 1245504 z^2 + 1413048 z^3 + 943392 z^4 + 344448 z^5 + 53248 z^6) 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]