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Search: id:A097663
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| A097663 |
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Decimal expansion of the constant 3*exp(psi(1/3)+EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620). |
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+0
15
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| 2, 3, 3, 1, 1, 9, 0, 9, 3, 1, 8, 4, 5, 6, 4, 1, 1, 7, 3, 0, 5, 3, 7, 5, 6, 2, 3, 2, 6, 5, 4, 4, 2, 8, 9, 5, 7, 4, 4, 6, 0, 8, 5, 8, 7, 0, 2, 5, 9, 2, 4, 5, 6, 4, 1, 4, 0, 9, 6, 0, 0, 7, 8, 7, 5, 6, 1, 6, 8, 2, 8, 5, 3, 1, 1, 5, 3, 1, 7, 4, 6, 3, 3, 5, 1, 1, 2, 2, 5, 5, 6, 6, 9, 4, 0, 6, 7, 7, 7, 0, 3, 3, 8, 9, 8
(list; cons; graph; listen)
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OFFSET
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1,1
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COMMENT
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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 A097677 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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Benoit Cloitre, On a generalization of Euler-Gauss formula for the Gamma function, pre-print 2004.
Xavier Gourdon and Pascal Sebah, Introduction to the Gamma Function.
Andrew Odlyzko, Asymptotic enumeration methods, in Handbook of Combinatorics, vol. 2, 1995, pp. 1063-1229.
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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 = 0.23311909318456411730537562326544289574460858702592456414096...
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MATHEMATICA
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RealDigits[1/Sqrt[3]*E^(-Pi/Sqrt[12]), 10, 105][[1]] (from Robert G. Wilson v Aug 28 2004)
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PROGRAM
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(PARI) 3*exp(psi(1/3)+Euler)
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CROSSREFS
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Cf. A001620, A047787, A097664, A097665-A097676.
Sequence in context: A005135 A139460 A105244 this_sequence A066517 A108132 A106589
Adjacent sequences: A097660 A097661 A097662 this_sequence A097664 A097665 A097666
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KEYWORD
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cons,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Aug 25 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 28 2004
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