OFFSET
1,3
COMMENTS
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..3000
Junyong Zhao, Shaofang Hong, and Xiao Jiang, A certain reciprocal power sum is never an integer, arXiv:1812.08705 [math.NT], 2018. See the constant alpha_f.
FORMULA
Equals (Pi*coth(Pi)-1)/2. - Vaclav Kotesovec, Jun 27 2015
Equals Integral_{x>=0} sin(x)/(exp(x) - 1) dx. - Amiram Eldar, Aug 16 2020
Equals Integral_{x>=0} (sin(x)/sinh(x))^2 dx. - Amiram Eldar, Dec 11 2023
EXAMPLE
1.07667404746858117413405079475000049044565626640381666557
MAPLE
evalf[120]((Pi*coth(Pi)-1)/2); # Muniru A Asiru, Dec 21 2018
MATHEMATICA
N[Sum[1/(k^2+1), {k, Infinity}], 1000]//RealDigits//First
PROG
(PARI) (Pi*cosh(Pi)/sinh(Pi)-1)/2 \\ Michel Marcus, Jun 28 2015
(PARI) sumnumrat(1/(x^2+1), 1) \\ Charles R Greathouse IV, Jan 20 2022
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
José María Grau Ribas, Jun 19 2015
STATUS
approved