A097667 Decimal expansion of the constant 5*exp(psi(1/5) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function.

0, 4, 4, 9, 4, 1, 8, 2, 8, 7, 7, 9, 2, 0, 8, 8, 2, 0, 6, 0, 8, 4, 6, 7, 3, 9, 6, 4, 2, 7, 6, 6, 5, 2, 0, 3, 4, 0, 2, 3, 8, 5, 9, 4, 3, 7, 1, 0, 5, 9, 8, 6, 9, 8, 0, 5, 8, 6, 1, 6, 7, 2, 9, 6, 3, 2, 5, 8, 8, 5, 3, 0, 7, 8, 6, 1, 2, 5, 6, 2, 7, 4, 7, 6, 8, 5, 8, 5, 5, 0, 9, 5, 9, 6, 1, 7, 3, 8, 6, 8, 6, 0, 8, 4, 4

Offset

0,2

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 = 0.04494182877920882060846739642766520340238594371059869805861...

Mathematica

RealDigits[ GoldenRatio^(-Sqrt[5]/2)/5^(1/4)*E^(-Pi/2*Sqrt[1 + 2/Sqrt[5]]), 10, 104][[1]] (* Robert G. Wilson v, Aug 27 2004 *)
Join[{0}, RealDigits[N[5*Exp[PolyGamma[1/5] + EulerGamma], 120], 10, 100][[1]]] (* G. C. Greubel, Dec 31 2016 *)

Prog

(PARI) 5*exp(psi(1/5)+Euler)

Crossrefs

Cf. A097663-A097666, A097668-A097676.

Sequence in context: A263491 A272427 A068340 * A202388 A283919 A283670

Adjacent sequences: A097664 A097665 A097666 * A097668 A097669 A097670

Keyword

cons,nonn

Author

Paul D. Hanna, Aug 25 2004

Extensions

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

Status

approved