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A097666 Decimal expansion of the constant 4*exp(psi(3/4) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function. 4
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; 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-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 = 1..2500

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]] (* Robert G. Wilson v, Aug 27 2004 *)

PROG

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

(MAGMA) SetDefaultRealField(RealField(100)); R:= RealField(); Exp(Pi(R)/2)/2; // G. C. Greubel, Sep 07 2018

CROSSREFS

Cf. A097663-A097665, A097667-A097676.

Sequence in context: A221087 A279580 A197513 * A144810 A300753 A319275

Adjacent sequences:  A097663 A097664 A097665 * A097667 A097668 A097669

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 11 20:03 EDT 2020. Contains 335652 sequences. (Running on oeis4.)