A097664 Decimal expansion of the constant 3*exp(psi(2/3) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function.

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

Offset

1,2

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-3 linear recursions with varying coefficients (see A097678 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.

Andrew Odlyzko, Asymptotic enumeration methods, in Handbook of Combinatorics, vol. 2, 1995, pp. 1063-1229.

Xavier Gourdon and Pascal Sebah, Introduction to the Gamma Function.

Formula

c = 1/sqrt(3)*exp(Pi/sqrt(12)).

Example

c = 1.42988430840123420566179042477513809656498236767564464887634...

Mathematica

RealDigits[1/Sqrt[3]*E^(Pi/Sqrt[12]), 10, 105][[1]] (* Robert G. Wilson v, Aug 28 2004 *)

Prog

(PARI) 3*exp(psi(2/3)+Euler)
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (1/Sqrt(3))*Exp(Pi(R)/Sqrt(12)); // G. C. Greubel, Aug 27 2018

Crossrefs

Cf. A097663, A097665-A097676.

Sequence in context: A249327 A182728 A290538 * A144811 A185654 A228041

Adjacent sequences: A097661 A097662 A097663 * A097665 A097666 A097667

Keyword

cons,nonn

Author

Paul D. Hanna, Aug 25 2004

Extensions

More terms from Robert G. Wilson v, Aug 28 2004

Status

approved