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Search: id:A097668
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| A097668 |
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Decimal expansion of the constant 5*exp(psi(2/5)+EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620). |
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+0
3
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| 6, 8, 7, 4, 7, 4, 2, 0, 6, 9, 9, 0, 8, 0, 1, 9, 6, 0, 7, 0, 8, 1, 6, 4, 2, 2, 1, 3, 3, 3, 9, 8, 4, 7, 5, 4, 9, 9, 7, 7, 7, 3, 5, 3, 0, 7, 8, 3, 2, 0, 5, 9, 3, 2, 3, 7, 3, 2, 7, 7, 5, 7, 1, 6, 4, 9, 6, 1, 3, 3, 4, 7, 9, 6, 8, 5, 6, 6, 7, 4, 7, 1, 1, 0, 0, 0, 9, 9, 2, 6, 7, 4, 2, 8, 4, 8, 2, 0, 1, 6, 9, 7, 8, 0, 8
(list; cons; graph; listen)
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OFFSET
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0,1
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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-5 linear recursions with varying coefficients (see A097680 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 = ((sqrt(5)+1)/2)^(sqrt(5)/2)/5^(1/4)*exp(-Pi/2*sqrt(1-2/sqrt(5)))
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EXAMPLE
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c = 0.68747420699080196070816422133398475499777353078320593237327...
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MATHEMATICA
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RealDigits[ GoldenRatio^(Sqrt[5]/2)/5^(1/4)*E^(-Pi/2Sqrt[1 - 2/Sqrt[5]]), 10, 105][[1]] (from Robert G. Wilson v Aug 27 2004)
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PROGRAM
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(PARI) 5*exp(psi(2/5)+Euler)
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CROSSREFS
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Cf. A097663-A097667, A097669-A097676.
Sequence in context: A019797 A141793 A092294 this_sequence A133748 A157852 A088608
Adjacent sequences: A097665 A097666 A097667 this_sequence A097669 A097670 A097671
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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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