OFFSET
0,3
REFERENCES
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 1 (Overseas Publishers Association, Amsterdam, 1986), p. 722, section 5.3.5, formula 9.
LINKS
Bruce C. Berndt and K. Venkatachaliengar, On the transformation formula for the Dedekind eta-function, in: F. G. Garvan and M. E. H. Ismail (eds.), Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics, eds., Kluwer, Dordrecht, 2001, pp. 73-77; preprint.
Mark W. Coffey, Bernoulli identities, zeta relations, determinant expressions, Mellin transforms, and representation of the Hurwitz numbers, Journal of Number Theory, Vol. 184 (2018), pp. 27-67, see Lemma 2, p. 62; arXiv preprint, arXiv:1601.01673 [math.NT], 2016, see Lemma 2, p. 33.
Eric Weisstein's World of Mathematics, Hyperbolic Cosecant.
FORMULA
Equals -Sum_{k>=1} 1/sin(k*Pi*i)^2. - Michel Marcus, Jan 11 2016
Equals Sum_{k>=1} 1/sinh(k*Pi)^2. - Vaclav Kotesovec, May 19 2022
EXAMPLE
0.007511723574771330897...
MATHEMATICA
RealDigits[1/6 - 1/(2*Pi), 10, 120, -1][[1]] (* Amiram Eldar, Jun 15 2023 *)
PROG
(PARI) -1/(2*Pi) + 1/6 \\ Michel Marcus, Jan 11 2016
(PARI) -suminf(k=1, 1/sin(k*Pi*I)^2) \\ Michel Marcus, Jan 11 2016
(PARI) suminf(k=1, 1/sinh(k*Pi)^2) \\ Vaclav Kotesovec, May 19 2022
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Eric W. Weisstein, Jul 15 2005
STATUS
approved