OFFSET
0,2
REFERENCES
Marius Iosifescu, and Cor Kraaikamp, Metrical Theory of Continued Fractions, Springer, 2002, p. 134.
LINKS
Hervé Daudé, Philippe Flajolet and Brigitte Vallée, An analysis of the Gaussian algorithm for lattice reduction, in: L. M. Adleman and M. D. Huang (eds.), Algorithmic Number Theory, First International Symposium, ANTS-I Ithaca, NY, USA, May 6-9, 1994, Proceedings, Lecture Notes in Computer Science, Vol. 877, Springer, Berlin, Heidelberg, 1994, pp. 144-158; Inria preprint.
Hervé Daudé, Philippe Flajolet and Brigitte Vallée, An average-case analysis of the Gaussian algorithm for lattice reduction, Combinatorics, Probability and computing, Vol. 6, No. 4 (1997), pp. 397-433; Inria preprint.
FORMULA
From Amiram Eldar, May 27 2021: (Start)
Equals Sum_{m>=1} 1/(tau(m)^4 + tau(m)^2), where tau(m) = (m + sqrt(m^2+4))/2.
Equals 7/2 - 7/(2*sqrt(2)) - 2/sqrt(5) - (1/2) * Sum_{k>=2} (-1)^k * binomial(2*k,k)*(zeta(2*k) - 1 - 1/2^(2*k))*(k - 1)/(k + 1). (End)
EXAMPLE
0.14446239624616081588249909052548320381...
MATHEMATICA
RealDigits[7/2 - 7/(2 Sqrt[2]) - 2/Sqrt[5] + NSum[(-1)^k * Binomial[2*k, k]*(Zeta[2*k] - 1 - 1/2^(2*k))*(k - 1)/(k + 1), {k, 1, Infinity}, Method -> "AlternatingSigns", WorkingPrecision -> 500]/2, 10, 100][[1]] (* Amiram Eldar, May 27 2021 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
N. J. A. Sloane, Sep 15 2002
EXTENSIONS
Offset corrected and more terms added by Amiram Eldar, May 27 2021
STATUS
approved