A364618 Decimal expansion of Sum_{k>=0} erfc(k), where erfc(x) is the complementary error function.
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, 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, 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
Offset: 1
Examples
1.16199904794712636353230832245579717116634350622586...
Links
- Tyma Gaidash, John Barber, and Steven Clark, How to evaluate Sum_{x=0..oo} erfc(x) = 1.1619990479471263635323...?, Mathematics StackExchange, 2021.
- Eric Weisstein's World of Mathematics, Dawson's Integral.
- Eric Weisstein's World of Mathematics, Erfc.
- Wikipedia, Dawson function.
- Wikipedia, Error function.
Crossrefs
Cf. A099287.
Programs
-
Maple
evalf(sum(erfc(k), k = 0 .. infinity), 120)
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Mathematica
RealDigits[N[Sum[Erfc[k], {k, 0, Infinity}], 120]][[1]] -
PARI
sumpos(k = 0, erfc(k))
Formula
Equals 1 + (2/Pi) * Integral_{x>=1} floor(x) * exp(-x^2) dx.
Equals 1/2 + 1/sqrt(Pi) + (4/sqrt(Pi)) * Sum_{k>=1} D(Pi*k)/(Pi*k), where D(x) is the Dawson function.
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