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A097674 Decimal expansion of the constant 8*exp(psi(3/8) + EulerGamma), where EulerGamma is the Euler-Mascheroni constant (A001620) and psi(x) is the digamma function. 3
9, 0, 7, 2, 4, 5, 8, 1, 7, 8, 8, 2, 1, 6, 4, 6, 0, 7, 5, 3, 8, 7, 9, 4, 5, 2, 4, 7, 9, 2, 0, 8, 1, 2, 1, 3, 7, 8, 7, 7, 7, 5, 2, 5, 4, 2, 3, 5, 8, 7, 4, 9, 5, 9, 0, 6, 8, 7, 1, 8, 5, 3, 7, 9, 4, 1, 1, 7, 5, 9, 2, 2, 5, 6, 2, 2, 2, 4, 4, 6, 9, 0, 5, 4, 4, 4, 2, 7, 0, 6, 8, 3, 1, 3, 0, 4, 9, 1, 8, 7, 8, 8, 7, 0, 9 (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-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
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*(sqrt(2)-1)).
EXAMPLE
c = 0.90724581788216460753879452479208121378777525423587495906871...
MATHEMATICA
RealDigits[(1 + Sqrt[2])^(Sqrt[2])/2E^(-Pi/2*(Sqrt[2] - 1)), 10, 105][[1]] (* Robert G. Wilson v, Aug 27 2004 *)
PROG
(PARI) 8*exp(psi(3/8)+Euler)
CROSSREFS
Sequence in context: A198213 A093766 A363368 * A309823 A196549 A173164
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 March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)