A097675 Decimal expansion of the constant 8*exp(psi(5/8) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function.

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

Offset

1,1

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 = 1..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 = 3.33325212658541721540039076972102211743980259727655469662827...

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(5/8)+Euler)

Crossrefs

Cf. A097663-A097674, A097676.

Sequence in context: A337265 A177228 A247655 * A141605 A356002 A251551

Adjacent sequences: A097672 A097673 A097674 * A097676 A097677 A097678

Keyword

cons,nonn

Author

Paul D. Hanna, Aug 25 2004

Extensions

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

Status

approved