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

1,3

Links

Table of n, a(n) for n=1..105.

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.

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

Example

1.16199904794712636353230832245579717116634350622586...

Maple

evalf(sum(erfc(k), k = 0 .. infinity), 120)

Mathematica

RealDigits[N[Sum[Erfc[k], {k, 0, Infinity}], 120]][[1]]

Prog

(PARI) sumpos(k = 0, erfc(k))

Crossrefs

Cf. A099287.

Sequence in context: A374948 A155079 A153608 * A340041 A073446 A097179

Adjacent sequences: A364615 A364616 A364617 * A364619 A364620 A364621

Keyword

nonn,cons,changed

Author

Amiram Eldar, Jul 30 2023

Status

approved