A097668 Decimal expansion of the constant 5*exp(psi(2/5)+EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function.

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

Offset

0,1

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-5 linear recursions with varying coefficients (see A097680 for example).

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.

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500

Benoit Cloitre, On a generalization of Euler-Gauss formula for the Gamma function, preprint 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.

Formula

c = ((sqrt(5)+1)/2)^(sqrt(5)/2)/5^(1/4)*exp(-Pi/2*sqrt(1-2/sqrt(5))).

Example

c = 0.68747420699080196070816422133398475499777353078320593237327...

Mathematica

RealDigits[ GoldenRatio^(Sqrt[5]/2)/5^(1/4)*E^(-Pi/2Sqrt[1 - 2/Sqrt[5]]), 10, 105][[1]] (* Robert G. Wilson v, Aug 27 2004 *)

Prog

(PARI) 5*exp(psi(2/5)+Euler)

Crossrefs

Cf. A097663-A097667, A097669-A097676.

Sequence in context: A283182 A198127 A092294 * A133748 A225037 A157852

Adjacent sequences: A097665 A097666 A097667 * A097669 A097670 A097671

Keyword

cons,nonn

Author

Paul D. Hanna, Aug 25 2004

Extensions

More terms from Robert G. Wilson v, Aug 27 2004

Status

approved