A110191 Decimal expansion of 1/6 - 1/(2*Pi).

0, 0, 7, 5, 1, 1, 7, 2, 3, 5, 7, 4, 7, 7, 1, 3, 3, 0, 8, 9, 7, 7, 8, 2, 9, 0, 3, 2, 9, 4, 1, 5, 2, 3, 0, 4, 6, 3, 2, 2, 0, 7, 0, 2, 0, 9, 2, 6, 2, 1, 0, 2, 1, 7, 9, 1, 8, 9, 9, 9, 3, 2, 2, 6, 0, 7, 7, 6, 9, 8, 6, 9, 0, 3, 2, 4, 4, 0, 1, 3, 1, 5, 7, 6, 5, 5, 2, 8, 6, 3, 9, 0, 0, 4, 1, 3, 5, 8, 0, 7, 1, 0

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

Table of n, a(n) for n=0..101.

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.

Index entries for transcendental numbers.

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

Cf. A086201.

Sequence in context: A145176 A093205 A156536 * A233090 A254177 A021575

Adjacent sequences: A110188 A110189 A110190 * A110192 A110193 A110194

Keyword

nonn,cons

Author

Eric W. Weisstein, Jul 15 2005

Status

approved