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A259171 Decimal expansion of Sum_{m>=1} 1/(m^2 + 1). 20
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Essentially the same as A100554 and A113319. - R. J. Mathar, Jul 06 2015
LINKS
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
Sequence in context: A290570 A073084 A011473 * A021570 A242977 A247314
KEYWORD
nonn,cons
AUTHOR
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)