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A097666 Decimal expansion of the constant 4*exp(psi(3/4)+EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620). +0
3
2, 4, 0, 5, 2, 3, 8, 6, 9, 0, 4, 8, 2, 6, 7, 5, 8, 2, 7, 7, 3, 6, 5, 1, 7, 8, 3, 3, 3, 5, 1, 9, 1, 6, 5, 6, 3, 1, 9, 5, 0, 8, 5, 4, 3, 7, 3, 3, 2, 2, 6, 7, 4, 7, 0, 0, 1, 0, 4, 0, 7, 7, 4, 4, 6, 2, 1, 2, 7, 5, 9, 5, 2, 4, 4, 5, 7, 9, 1, 0, 6, 8, 3, 7, 4, 3, 5, 2, 3, 8, 3, 2, 9, 1, 9, 4, 1, 6, 7, 7, 3, 2, 8, 6, 4 (list; cons; graph; listen)
OFFSET

1,1

COMMENT

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

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 = 1/2*exp(Pi/2)

EXAMPLE

c = 2.40523869048267582773651783335191656319508543733226747001040...

MATHEMATICA

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

PROGRAM

(PARI) 4*exp(psi(3/4)+Euler)

CROSSREFS

Cf. A097663-A097665, A097667-A097676.

Adjacent sequences: A097663 A097664 A097665 this_sequence A097667 A097668 A097669

Sequence in context: A086932 A079985 A059226 this_sequence A002652 A070676 A068451

KEYWORD

cons,nonn

AUTHOR

Paul D. Hanna (pauldhanna(AT)juno.com), Aug 25 2004

EXTENSIONS

More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 27 2004

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Last modified October 13 09:05 EDT 2008. Contains 145008 sequences.


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