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

*To*: mathgroup at smc.vnet.net*Subject*: [mg126610] Re: Function Exp[x^2]*Erfc[x]*From*: Szabolcs <szhorvat at gmail.com>*Date*: Fri, 25 May 2012 04:55:48 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <jhldom$ov9$1@smc.vnet.net>

On Friday, 17 February 2012 12:30:30 UTC+1, Leslaw Bieniasz 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 There is a discussion of this function here: http://mathematica.stackexchange.com/q/3854/12 You might be interested in it. There doesn't seem to be a built-in way to evaluate it directly, but the page I linked to has implementations of several methods to calculate it.