A362753 Decimal expansion of Sum_{k>=1} sin(1/k)/k.
1, 4, 7, 2, 8, 2, 8, 2, 3, 1, 9, 5, 6, 1, 8, 5, 2, 9, 6, 2, 9, 4, 9, 4, 7, 3, 8, 3, 8, 2, 3, 1, 4, 5, 8, 2, 5, 3, 2, 3, 8, 6, 5, 9, 2, 7, 8, 7, 9, 3, 0, 7, 1, 7, 2, 8, 1, 9, 2, 2, 9, 3, 7, 5, 7, 2, 2, 4, 3, 3, 9, 0, 6, 1, 0, 1, 1, 5, 7, 2, 2, 0, 8, 1, 5, 1, 3, 5, 5, 0, 7, 0, 4, 1, 5, 0, 6, 8, 9, 1, 3, 3, 2, 7, 5
Offset: 1
Examples
1.47282823195618529629494738382314582532386592787930...
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.
Programs
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Maple
evalf(sum(sin(1/k)/k, k = 1 .. infinity), 120);
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PARI
sumpos(k = 1, sin(1/k)/k)
Formula
Equals Sum_{k>=1} (-1)^(k+1)*zeta(2*k)/(2*k-1)!.
Comments