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A097672
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Decimal expansion of the constant 6*exp(psi(5/6)+EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620).
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2
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4, 3, 8, 5, 2, 4, 5, 9, 8, 6, 2, 5, 0, 8, 0, 8, 1, 7, 3, 6, 9, 9, 4, 8, 9, 9, 4, 3, 2, 2, 9, 5, 6, 2, 0, 7, 7, 6, 5, 0, 8, 0, 1, 2, 8, 5, 0, 0, 9, 0, 2, 7, 6, 3, 0, 4, 2, 0, 0, 6, 5, 5, 4, 6, 7, 7, 6, 4, 3, 3, 1, 5, 6, 4, 6, 0, 8, 4, 8, 1, 1, 5, 4, 4, 3, 9, 9, 7, 3, 9, 5, 5, 1, 5, 6, 0, 8, 7, 7, 8, 8, 4, 6, 6, 7
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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-6 linear recursions with varying coefficients (see A097681 for example).
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REFERENCES
| 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
| 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
| c = 1/sqrt(12)*exp(Pi/2*sqrt(3))
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EXAMPLE
| c = 4.38524598625080817369948994322956207765080128500902763042006...
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MATHEMATICA
| RealDigits[1/Sqrt[12]*E^(Pi/2Sqrt[3]), 10, 105][[1]] (from Robert G. Wilson v Aug 27 2004)
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PROG
| (PARI) 6*exp(psi(5/6)+Euler)
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CROSSREFS
| Cf. A097663-A097671, A097673-A097676.
Sequence in context: A019835 A200345 A021962 * A103339 A092383 A156028
Adjacent sequences: A097669 A097670 A097671 * A097673 A097674 A097675
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KEYWORD
| cons,nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Aug 25 2004
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 27 2004
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