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%I #13 May 20 2022 05:59:49
%S 1,5,7,8,4,7,7,5,7,9,6,6,7,1,3,6,8,3,8,3,1,8,0,2,2,1,9,3,2,4,5,7,1,9,
%T 2,3,5,0,4,6,6,7,2,2,1,7,3,2,7,2,9,1,3,2,7,5,8,7,4,8,6,6,4,5,7,9,3,8,
%U 0,8,4,4,8,0,6,1,6,8,1,1,1,7,4,5,7,3,1,9,4,3,5,4,1,6,6,6,2,8,6,3,8,3,1,6,6
%N Decimal expansion of Sum_{k>=0} 1 / (k^4 + 1).
%C Apart from leading digits the same as A256920. - _R. J. Mathar_, May 20 2022
%F Equals 1/2 + (Pi*(sinh(sqrt(2)*Pi) + sin(sqrt(2)*Pi))) / (2*sqrt(2)*(cosh(sqrt(2)*Pi) - cos(sqrt(2)*Pi))).
%e 1.578477579667136838318022193245719235046672217327291327587486645793808...
%p evalf(1/2 + (Pi*(sinh(sqrt(2)*Pi) + sin(sqrt(2)*Pi))) / (2*sqrt(2)*(cosh(sqrt(2)*Pi) - cos(sqrt(2)*Pi))), 105);
%t RealDigits[Chop[N[Sum[1/(k^4 + 1), {k, 0, Infinity}], 105]]][[1]]
%o (PARI) sumpos(k=0, 1/(k^4 + 1))
%Y Cf. A256920, A113319, A354052, A354053.
%Y Cf. A002523, A255434, A354004.
%K nonn,cons
%O 1,2
%A _Vaclav Kotesovec_, May 16 2022, following a suggestion from _Bernard Schott_