A257526 Decimal expansion of e*Pi*erfc(1).

1, 3, 4, 3, 2, 9, 3, 4, 2, 1, 6, 4, 6, 7, 3, 5, 1, 7, 0, 4, 3, 7, 1, 2, 3, 5, 9, 4, 4, 1, 0, 5, 8, 9, 7, 7, 8, 3, 2, 2, 8, 2, 9, 5, 6, 7, 1, 3, 0, 0, 3, 6, 8, 7, 2, 0, 5, 1, 9, 5, 5, 5, 6, 4, 5, 5, 3, 0, 2, 5, 8, 2, 7, 9, 6, 9, 7, 2, 7, 7, 5, 7, 9, 8, 4, 1, 3, 3, 5, 0, 0, 7, 6, 5, 4, 8, 8, 0, 0, 2, 5, 4, 9

Offset

1,2

Links

Table of n, a(n) for n=1..103.

MathOverflow, Contour integration problem from probability

Eric Weisstein's MathWorld, Erfc

Formula

Equals Integral_{-infinity..infinity} exp(-x^2)/(1+x^2) dx.

Also equals J(0) where J(c) = Integral_{-infinity..infinity} exp(-(x-c)^2)/(1+x^2) dx = (1/2)*Pi*e*(erfc[1-c*i]*e^(-2*c*i) + erfc[1+c*i]*e^(2*c*i)), where the integrand comes from a shifted normal PDF times a Cauchy PDF.

Equals 2 * Integral_{x=0..Pi/2} exp(-tan(x)^2) dx. - Amiram Eldar, Aug 07 2020

Example

1.343293421646735170437123594410589778322829567130036872051955564553...

Mathematica

RealDigits[E*Pi*Erfc[1], 10, 103] // First

Prog

(PARI) exp(1)*Pi*erfc(1) \\ Charles R Greathouse IV, Apr 18 2016

Crossrefs

Cf. A099287, A108088.

Sequence in context: A133617 A199286 A188722 * A038774 A092910 A356334

Adjacent sequences: A257523 A257524 A257525 * A257527 A257528 A257529

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 28 2015

Status

approved