Re: Function Exp[x^2]*Erfc[x]

*To*: mathgroup at smc.vnet.net*Subject*: [mg125018] Re: Function Exp[x^2]*Erfc[x]*From*: Ray Koopman <koopman at sfu.ca>*Date*: Sat, 18 Feb 2012 06:23:33 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jhldom$ov9$1@smc.vnet.net>

On Feb 17, 3:30 am, Leslaw Bieniasz <nbbie... at cyf-kr.edu.pl> wrote: > Hi, > > MATHEMATICA is supposed to contain all known rules from tables of > functions etc. One of the very important special functions, related > to the function w(z) defined (for example) in Abramowitz and Stegun book, > is Exp[x^2]*Erfc[x]. Although it can be expressed formally as the product > of two other functions, Exp and Erfc, there is no effective way to compute > the values of the function in a wide range of x values, by using Exp and > Erfc, because of the overflow in Exp[]. There are known approximations > to Exp[x^2]*Erfc[x] (for example ones produced by Cody and co-workers > a few decades ago), but I don't see any support for the function in > MATHEMATICA. Is this indeed so, or I miss something? > > Leslaw Exp[x^2]*Erfc[x] = 2/(Sqrt[Pi]* HazardFunction[NormalDistribution[0,Sqrt[1/2]],x])