OFFSET
1,2
COMMENTS
The value of the Hardy-Littlewood function H(x) = Sum_{k>=1} sin(x/k)/k at x = 1 (Hardy and Littlewood, 1936; Gautschi, 2004).
REFERENCES
Walter Gautschi, Orthogonal Polynomials: Computation and Approximation, Oxford University Press, 2004. See Example 3.64, pp. 242-245.
LINKS
Kara Garrison and Thomas E. Price, Approximating Sums of Infinite Series, 17th Biennial ACMS Conference MAY 27-30, 2009, Conference Proceedings (2009), pp. 74-83.
G. H. Hardy and J. E. Littlewood, Notes on the theory of series (xx): On Lambert series, Proc. London Math. Soc., Vol. s2-41, Issue 1 (1936), pp. 257-270.
Math Stackexchange, Does the series Sum_{k=1..n} sin(1/k)/k converge?, 2017.
FORMULA
Equals Sum_{k>=1} (-1)^(k+1)*zeta(2*k)/(2*k-1)!.
EXAMPLE
1.47282823195618529629494738382314582532386592787930...
MAPLE
evalf(sum(sin(1/k)/k, k = 1 .. infinity), 120);
PROG
(PARI) sumpos(k = 1, sin(1/k)/k)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, May 02 2023
STATUS
approved