A259171 Decimal expansion of Sum_{m>=1} 1/(m^2 + 1).

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

Offset: 1

Author

José María Grau Ribas, Jun 19 2015

Keywords

• nonn
• cons

Comments

Essentially the same as A100554 and A113319. - R. J. Mathar, Jul 06 2015

Examples

			1.07667404746858117413405079475000049044565626640381666557
		

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.

Crossrefs

Cf. A013661, A259173.

Programs

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

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

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