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MathGroup Archive 2012

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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])



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