Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.6647)

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=-5/3, b>=a

For fixed z and a=-5/3, b=2/3

http://functions.wolfram.com/07.23.03.6647.01

Input Form

Hypergeometric2F1[-(5/3), 2/3, 11/2, -z] == (6561 (Sqrt[z] (-22680 - 161160 z - 499352 z^2 - 900392 z^3 - 294363 z^4 + 279565 z^5 + 34408 z^6) Cosh[ArcSinh[Sqrt[z]]/3] + Sqrt[1 + z] (68040 + 463320 z + 1369736 z^2 + 2351032 z^3 + 3120120 z^4 + 262361 z^5 + 34408 z^6) Sinh[ArcSinh[Sqrt[z]]/3]))/ (6092560045 z^(9/2) 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]