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
Examples
1.343293421646735170437123594410589778322829567130036872051955564553...
Links
- MathOverflow, Contour integration problem from probability
- Eric Weisstein's MathWorld, Erfc
Programs
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Mathematica
RealDigits[E*Pi*Erfc[1], 10, 103] // First
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PARI
exp(1)*Pi*erfc(1) \\ Charles R Greathouse IV, Apr 18 2016
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