A257526 - OEIS

%I #13 Aug 07 2020 11:07:26

%S 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,

%T 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,

%U 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

%N Decimal expansion of e*Pi*erfc(1).

%H MathOverflow, <a href="http://mathoverflow.net/questions/37107">Contour integration problem from probability </a>

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/Erfc.html">Erfc </a>

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

%F 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.

%F Equals 2 * Integral_{x=0..Pi/2} exp(-tan(x)^2) dx. - _Amiram Eldar_, Aug 07 2020

%e 1.343293421646735170437123594410589778322829567130036872051955564553...

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

%o (PARI) exp(1)*Pi*erfc(1) \\ _Charles R Greathouse IV_, Apr 18 2016

%Y Cf. A099287, A108088.

%K nonn,cons,easy

%O 1,2

%A _Jean-François Alcover_, Apr 28 2015