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A364618 Decimal expansion of Sum_{k>=0} erfc(k), where erfc(x) is the complementary error function.

%I A364618 #17 Oct 11 2024 07:09:48
%S A364618 1,1,6,1,9,9,9,0,4,7,9,4,7,1,2,6,3,6,3,5,3,2,3,0,8,3,2,2,4,5,5,7,9,7,
%T A364618 1,7,1,1,6,6,3,4,3,5,0,6,2,2,5,8,6,8,0,3,1,2,1,6,8,2,6,3,3,2,4,1,5,9,
%U A364618 4,1,7,5,5,0,4,9,4,0,0,2,3,8,6,4,7,8,1,3,2,8,3,6,2,6,2,8,9,3,3,5,1,8,4,4,7
%N A364618 Decimal expansion of Sum_{k>=0} erfc(k), where erfc(x) is the complementary error function.
%H A364618 Tyma Gaidash, John Barber, and Steven Clark, <a href="https://math.stackexchange.com/questions/4255028/how-to-evaluate-sum-limits-x-0-infty-texterfcx-1-16199904794712636353">How to evaluate Sum_{x=0..oo} erfc(x) = 1.1619990479471263635323...?</a>, Mathematics StackExchange, 2021.
%H A364618 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DawsonsIntegral.html">Dawson's Integral</a>.
%H A364618 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Erfc.html">Erfc</a>.
%H A364618 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dawson_function">Dawson function</a>.
%H A364618 Wikipedia, <a href="https://en.wikipedia.org/wiki/Error_function">Error function</a>.
%F A364618 Equals 1 + (2/Pi) * Integral_{x>=1} floor(x) * exp(-x^2) dx.
%F A364618 Equals 1/2 + 1/sqrt(Pi) + (4/sqrt(Pi)) * Sum_{k>=1} D(Pi*k)/(Pi*k), where D(x) is the Dawson function.
%F A364618 Equals (2/Pi)*Integral_{x=0..oo} (exp(x) - cos(x))*sin((x^2)/2)/(x*(cosh(x) - cos(x))) dx. - _Velin Yanev_, Oct 11 2024
%e A364618 1.16199904794712636353230832245579717116634350622586...
%p A364618 evalf(sum(erfc(k), k = 0 .. infinity), 120)
%t A364618 RealDigits[N[Sum[Erfc[k], {k, 0, Infinity}], 120]][[1]]
%o A364618 (PARI) sumpos(k = 0, erfc(k))
%Y A364618 Cf. A099287.
%K A364618 nonn,cons
%O A364618 1,3
%A A364618 _Amiram Eldar_, Jul 30 2023