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A097665 Decimal expansion of the constant 4*exp(psi(1/4) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function. 5
1, 0, 3, 9, 3, 9, 7, 8, 8, 1, 7, 5, 3, 8, 0, 9, 5, 4, 2, 7, 3, 4, 7, 7, 8, 0, 9, 9, 1, 7, 4, 8, 9, 3, 8, 5, 0, 1, 6, 9, 3, 8, 9, 2, 0, 8, 1, 5, 8, 8, 4, 8, 0, 4, 0, 3, 7, 5, 6, 7, 9, 4, 1, 5, 2, 7, 7, 0, 9, 9, 3, 8, 6, 4, 2, 7, 4, 1, 0, 6, 9, 8, 9, 4, 3, 0, 0, 1, 3, 8, 9, 3, 2, 7, 1, 3, 0, 1, 7, 6, 7, 0, 2, 6, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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-4 linear recursions with varying coefficients (see A097679 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..2500

Benoit Cloitre, On a generalization of Euler-Gauss formula for the Gamma function, pre-print 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 = 1/2*exp(-Pi/2).

EXAMPLE

c = 0.10393978817538095427347780991748938501693892081588480403756...

MATHEMATICA

RealDigits[1/2*E^(-Pi/2), 10, 105][[1]] (* Robert G. Wilson v, Aug 28 2004 *)

PROG

(PARI) 4*exp(psi(1/4)+Euler)

CROSSREFS

Cf. A097663-A097664, A097666-A097676.

Sequence in context: A268580 A179802 A010707 * A284564 A170862 A083996

Adjacent sequences:  A097662 A097663 A097664 * A097666 A097667 A097668

KEYWORD

cons,nonn

AUTHOR

Paul D. Hanna, Aug 25 2004

EXTENSIONS

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

STATUS

approved

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Last modified July 4 15:25 EDT 2020. Contains 335448 sequences. (Running on oeis4.)