A097670 Decimal expansion of the constant 5*exp(psi(4/5) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function.

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

Offset: 1

Author

Paul D. Hanna, Aug 25 2004

Keywords

• cons
• nonn

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).

Examples

			c = 3.39276427892784980770475505655447128392740109258608442234780...
		

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.

Crossrefs

Cf. A097663-A097669, A097671-A097676.

Programs

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 *)

PARI

5*exp(psi(4/5)+Euler)

Formula

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

Extensions

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