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A097664
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Decimal expansion of the constant 3*exp(psi(2/3) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function.
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4
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1, 4, 2, 9, 8, 8, 4, 3, 0, 8, 4, 0, 1, 2, 3, 4, 2, 0, 5, 6, 6, 1, 7, 9, 0, 4, 2, 4, 7, 7, 5, 1, 3, 8, 0, 9, 6, 5, 6, 4, 9, 8, 2, 3, 6, 7, 6, 7, 5, 6, 4, 4, 6, 4, 8, 8, 7, 6, 3, 4, 6, 2, 1, 4, 8, 8, 3, 6, 9, 9, 4, 5, 0, 9, 1, 2, 2, 0, 3, 9, 6, 1, 6, 1, 8, 2, 1, 9, 5, 9, 1, 4, 6, 9, 0, 1, 8, 4, 6, 3, 6, 2, 3, 7, 8
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OFFSET
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1,2
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COMMENTS
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This constant appears in Benoit Cloitre's generalized Euler-Gauss formula for the Gamma function (see Cloitre link) and is involved in the exact determination of asymptotic limits of certain order-3 linear recursions with varying coefficients (see A097678 for example).
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REFERENCES
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A. M. Odlyzko, Linear recurrences with varying coefficients, in Handbook of Combinatorics, Vol. 2, R. L. Graham, M. Grotschel and L. Lovasz, eds., Elsevier, Amsterdam, 1995, pp. 1135-1138.
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LINKS
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FORMULA
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c = 1/sqrt(3)*exp(Pi/sqrt(12)).
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EXAMPLE
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c = 1.42988430840123420566179042477513809656498236767564464887634...
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MATHEMATICA
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PROG
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(PARI) 3*exp(psi(2/3)+Euler)
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (1/Sqrt(3))*Exp(Pi(R)/Sqrt(12)); // G. C. Greubel, Aug 27 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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