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MathGroup Archive 2005

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Re: Help for an integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57356] Re: Help for an integral
  • From: "meznaric" <meznaric at gmail.com>
  • Date: Wed, 25 May 2005 06:03:06 -0400 (EDT)
  • References: <d6uspo$j5b$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

I think Mathematica uses the cumulative normal distribution function
automatically (calling it Erf[x]). If you say try x/Exp[a*(1 -
2*x^2)^2], it will return a solution in terms of Erf function. You
could also try a series solution, which would probably be in its
simplest form if developed around x=1/Sqrt[2]. So you can try:
int = Normal[Series[x^2/Exp[a*(1 - 2*x^2)^2],{x,1/Sqrt[2],10}]];
This will store the ten term Taylor series expansion into int and you
can integrate it to obtain a numerical approximation for this integral.

Well actually trying this out I found that NIntegrate works much better
for the purpose of numerical approximation.
If you wish to express the integral in terms of Erf, however, I am
afraid you will have to do it by hand, because Mathematica does not
seem able to do that (or there may be no way to do that).

Sebastjan


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