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A097674
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Decimal expansion of the constant 8*exp(psi(3/8)+EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620).
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2
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9, 0, 7, 2, 4, 5, 8, 1, 7, 8, 8, 2, 1, 6, 4, 6, 0, 7, 5, 3, 8, 7, 9, 4, 5, 2, 4, 7, 9, 2, 0, 8, 1, 2, 1, 3, 7, 8, 7, 7, 7, 5, 2, 5, 4, 2, 3, 5, 8, 7, 4, 9, 5, 9, 0, 6, 8, 7, 1, 8, 5, 3, 7, 9, 4, 1, 1, 7, 5, 9, 2, 2, 5, 6, 2, 2, 2, 4, 4, 6, 9, 0, 5, 4, 4, 4, 2, 7, 0, 6, 8, 3, 1, 3, 0, 4, 9, 1, 8, 7, 8, 8, 7, 0, 9
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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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-8 linear recursions with varying coefficients (see A097682 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(2))^(sqrt(2))/2*exp(-Pi/2*(sqrt(2)-1))
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EXAMPLE
| c = 0.90724581788216460753879452479208121378777525423587495906871...
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MATHEMATICA
| RealDigits[(1 + Sqrt[2])^(Sqrt[2])/2E^(-Pi/2*(Sqrt[2] - 1)), 10, 105][[1]] (from Robert G. Wilson v Aug 27 2004)
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PROG
| (PARI) 8*exp(psi(3/8)+Euler)
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CROSSREFS
| Cf. A097663-A097673, A097675-A097676.
Sequence in context: A131223 A198213 A093766 * A196549 A173164 A181446
Adjacent sequences: A097671 A097672 A097673 * A097675 A097676 A097677
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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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