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A097663 Decimal expansion of the constant 3*exp(psi(1/3) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function. 16
2, 3, 3, 1, 1, 9, 0, 9, 3, 1, 8, 4, 5, 6, 4, 1, 1, 7, 3, 0, 5, 3, 7, 5, 6, 2, 3, 2, 6, 5, 4, 4, 2, 8, 9, 5, 7, 4, 4, 6, 0, 8, 5, 8, 7, 0, 2, 5, 9, 2, 4, 5, 6, 4, 1, 4, 0, 9, 6, 0, 0, 7, 8, 7, 5, 6, 1, 6, 8, 2, 8, 5, 3, 1, 1, 5, 3, 1, 7, 4, 6, 3, 3, 5, 1, 1, 2, 2, 5, 5, 6, 6, 9, 4, 0, 6, 7, 7, 7, 0, 3, 3, 8, 9, 8 (list; constant; graph; refs; listen; history; text; internal format)
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-3 linear recursions with varying coefficients (see A097677 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..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(3)*exp(-Pi/sqrt(12)).

EXAMPLE

c = 0.23311909318456411730537562326544289574460858702592456414096...

MATHEMATICA

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

PROG

(PARI) 3*exp(psi(1/3)+Euler)

(MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); Exp(-Pi(R)/Sqrt(12))/Sqrt(3); // G. C. Greubel, Sep 07 2018

CROSSREFS

Cf. A001620, A047787, A097664, A097665-A097676.

Sequence in context: A257451 A209007 A145854 * A247565 A204259 A066517

Adjacent sequences:  A097660 A097661 A097662 * A097664 A097665 A097666

KEYWORD

cons,nonn

AUTHOR

Paul D. Hanna, Aug 25 2004

EXTENSIONS

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

Offset corrected by R. J. Mathar, Feb 05 2009

STATUS

approved

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Last modified July 12 06:48 EDT 2020. Contains 335657 sequences. (Running on oeis4.)