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

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, 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, 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

Offset

1,1

Links

Table of n, a(n) for n=1..96.

Les-mathematiques.net, Somme arctan(1/k).

Cornel Ioan Vălean, Problem 11924, The American Mathematical Monthly, Vol. 123, No. 7 (2016), p. 722; An Integral with Fractional Part of Tangent, Solution to Problem 11924 by Edward and Roberta White, ibid., Vol. 125, No. 5 (2018), pp. 468-470.

Formula

Equals log(Pi/sinh(Pi)) / 2.

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

Example

-0.65092319930185633888521683150394766...

Maple

evalf(log(Pi/sinh(Pi)) / 2, 100);

Mathematica

RealDigits[Log[Pi/Sinh[Pi]]/2, 10, 100][[1]] (* Amiram Eldar, Mar 19 2022 *)

Crossrefs

Cf. A013661, A002117, A013662, A090986.

Sequence in context: A193355 A248922 A316253 * A261992 A278760 A199724

Adjacent sequences: A352524 A352525 A352526 * A352528 A352529 A352530

Keyword

nonn,cons

Author

Bernard Schott, Mar 19 2022

Status

approved