OFFSET
1,2
LINKS
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
KEYWORD
AUTHOR
Jean-François Alcover, Apr 28 2015
STATUS
approved