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A097676 Decimal expansion of the constant 8*exp(psi(7/8) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function. 14
6, 3, 7, 6, 6, 3, 2, 4, 8, 9, 4, 1, 6, 6, 7, 7, 8, 5, 5, 0, 0, 1, 7, 6, 2, 5, 9, 3, 8, 2, 5, 1, 0, 7, 9, 0, 6, 2, 6, 7, 4, 3, 5, 3, 2, 6, 7, 8, 6, 4, 6, 2, 1, 6, 7, 6, 7, 3, 0, 6, 4, 1, 0, 7, 4, 3, 4, 2, 6, 4, 5, 4, 9, 1, 5, 2, 5, 9, 9, 9, 3, 9, 0, 8, 8, 3, 3, 7, 3, 3, 1, 6, 4, 3, 8, 3, 2, 7, 6, 5, 5, 5, 3, 4, 9 (list; constant; graph; refs; listen; history; text; internal format)
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..5000

Benoit Cloitre, On a generalization of Euler-Gauss formula for the Gamma function, pre-print 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*(1+sqrt(2))).

EXAMPLE

c = 6.37663248941667785500176259382510790626743532678646216767306...

MATHEMATICA

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

PROG

(PARI) 8*exp(psi(7/8)+Euler)

(MAGMA) SetDefaultRealField(RealField(100)); R:= RealField();

(1+Sqrt(2))^(-Sqrt(2))/2*Exp(Pi(R)/2*(1+Sqrt(2))); // G. C. Greubel, Sep 07 2018

CROSSREFS

Cf. A097663-A097675.

Sequence in context: A011191 A246730 A200239 * A251780 A249542 A125123

Adjacent sequences:  A097673 A097674 A097675 * A097677 A097678 A097679

KEYWORD

cons,nonn

AUTHOR

Paul D. Hanna, Aug 25 2004

EXTENSIONS

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

STATUS

approved

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Last modified July 4 12:56 EDT 2020. Contains 335448 sequences. (Running on oeis4.)