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Search: id:A097673
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| A097673 |
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Decimal expansion of the constant 8*exp(psi(1/8)+EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620). |
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+0
4
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| 0, 0, 3, 2, 4, 1, 1, 2, 2, 8, 3, 0, 0, 9, 6, 3, 0, 7, 3, 7, 4, 7, 5, 1, 1, 7, 1, 2, 1, 7, 9, 1, 9, 0, 1, 7, 0, 1, 0, 7, 3, 8, 4, 7, 9, 2, 2, 1, 5, 1, 0, 4, 0, 0, 6, 9, 2, 9, 9, 0, 5, 9, 2, 3, 0, 5, 1, 8, 5, 7, 1, 1, 0, 2, 1, 3, 7, 4, 1, 0, 1, 1, 3, 2, 7, 9, 8, 7, 0, 4, 4, 4, 3, 6, 4, 9, 4, 7, 3, 7, 7, 4, 7, 2, 2
(list; cons; graph; listen)
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OFFSET
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0,3
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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-8 linear recursions with varying coefficients (see A097682 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(2))^(-sqrt(2))/2*exp(-Pi/2*(1+sqrt(2)))
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EXAMPLE
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c = 0.00324112283009630737475117121791901701073847922151040069299...
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MATHEMATICA
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RealDigits[(1 + Sqrt[2])^(-Sqrt[2])/2E^(-Pi/2*(1 + Sqrt[2])), 10, 103][[1]] (from Robert G. Wilson v Aug 27 2004)
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PROGRAM
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(PARI) 8*exp(psi(1/8)+Euler)
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CROSSREFS
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Cf. A097663-A097672, A097674-A097676.
Sequence in context: A004545 A127481 A154879 this_sequence A140430 A123359 A121885
Adjacent sequences: A097670 A097671 A097672 this_sequence A097674 A097675 A097676
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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 27 2004
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