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Search: id:A097669
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| A097669 |
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Decimal expansion of the constant 5*exp(psi(3/5)+EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620). |
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+0
3
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| 1, 9, 0, 7, 9, 5, 9, 5, 3, 2, 5, 4, 3, 5, 4, 2, 5, 2, 2, 5, 5, 3, 3, 3, 8, 1, 3, 9, 7, 2, 9, 5, 2, 0, 3, 6, 9, 0, 8, 5, 1, 6, 0, 6, 8, 3, 5, 9, 0, 8, 2, 9, 6, 8, 2, 2, 8, 2, 2, 3, 5, 9, 6, 0, 8, 1, 0, 7, 0, 6, 3, 7, 8, 6, 8, 8, 6, 5, 5, 0, 4, 0, 3, 9, 9, 7, 2, 3, 6, 3, 5, 8, 3, 0, 9, 0, 1, 3, 8, 0, 7, 5, 3, 9, 0
(list; cons; graph; listen)
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OFFSET
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1,2
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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 = 1.90795953254354252255333813972952036908516068359082968228223...
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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(3/5)+Euler)
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CROSSREFS
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Cf. A097663-A097668, A097670-A097676.
Sequence in context: A131223 A093766 A097674 this_sequence A019820 A019985 A021995
Adjacent sequences: A097666 A097667 A097668 this_sequence A097670 A097671 A097672
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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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