cp's OEIS Frontend

A352527 Decimal expansion of Sum_(k>=1) (-1)^k * zeta(2k)/(2k) (negated).

%I A352527 #29 Feb 08 2024 02:00:17
%S A352527 6,5,0,9,2,3,1,9,9,3,0,1,8,5,6,3,3,8,8,8,5,2,1,6,8,3,1,5,0,3,9,4,7,6,
%T A352527 6,5,0,6,5,5,0,8,7,5,7,1,3,9,7,2,2,5,9,1,9,9,8,3,8,2,4,8,2,1,0,6,4,0,
%U A352527 7,4,3,1,1,3,0,4,9,6,7,0,7,0,6,4,5,5,8,5,9,5,0,9,4,0,9,4
%N A352527 Decimal expansion of Sum_(k>=1) (-1)^k * zeta(2k)/(2k) (negated).
%H A352527 Les-mathematiques.net, <a href="https://les-mathematiques.net/vanilla/index.php?p=discussion/comment/254775#Comment_254775">Somme arctan(1/k)</a>.
%H A352527 Cornel Ioan Vălean, <a href="https://www.jstor.org/stable/10.4169/amer.math.monthly.123.7.722">Problem 11924</a>, The American Mathematical Monthly, Vol. 123, No. 7 (2016), p. 722; <a href="https://www.jstor.org/stable/48663339">An Integral with Fractional Part of Tangent</a>, Solution to Problem 11924 by Edward and Roberta White, ibid., Vol. 125, No. 5 (2018), pp. 468-470.
%F A352527 Equals log(Pi/sinh(Pi)) / 2.
%F A352527 Equals Integral_{x=0..Pi/2} ({tan(x)}/tan(x) - 1) dx, where {x} = x - floor(x) is the fractional part of x (Vălean, 2016). - _Amiram Eldar_, Feb 08 2024
%e A352527 -0.65092319930185633888521683150394766...
%p A352527 evalf(log(Pi/sinh(Pi)) / 2, 100);
%t A352527 RealDigits[Log[Pi/Sinh[Pi]]/2, 10, 100][[1]] (* _Amiram Eldar_, Mar 19 2022 *)
%Y A352527 Cf. A013661, A002117, A013662, A090986.
%K A352527 nonn,cons
%O A352527 1,1
%A A352527 _Bernard Schott_, Mar 19 2022