Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.4890)

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=14/3

http://functions.wolfram.com/07.23.03.4890.01

Input Form

Hypergeometric2F1[-(17/3), 14/3, 9/2, -z] == (243 (Sqrt[z] (3672 - 14416 z + 86632 z^2 + 17934389 z^3 + 105631669 z^4 + 263227328 z^5 + 351257712 z^6 + 264041024 z^7 + 105913600 z^8 + 17704960 z^9) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[1 + z] (-11016 + 46512 z - 275128 z^2 + 4188800 z^3 + 47830497 z^4 + 158357056 z^5 + 253422000 z^6 + 217723584 z^7 + 97061120 z^8 + 17704960 z^9) Sinh[ArcSinh[Sqrt[z]]/3]))/ (4690180495 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]