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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.