A097674 Decimal expansion of the constant 8*exp(psi(3/8) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function.

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

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-8 linear recursions with varying coefficients (see A097682 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 = (1+sqrt(2))^(sqrt(2))/2*exp(-Pi/2*(sqrt(2)-1)).

Example

c = 0.90724581788216460753879452479208121378777525423587495906871...

Mathematica

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

Prog

(PARI) 8*exp(psi(3/8)+Euler)

Crossrefs

Cf. A097663-A097673, A097675-A097676.

Sequence in context: A198213 A093766 A363368 * A372830 A309823 A196549

Adjacent sequences: A097671 A097672 A097673 * A097675 A097676 A097677

Keyword

cons,nonn

Author

Paul D. Hanna, Aug 25 2004

Extensions

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

Status

approved