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Indefinite Integral

  1. Nov 23, 2004 #1
    I've been trying to integrate the following function but have gotten somewhat stuck doing it. The answer i managed to produce gave some bogan answers.

    the integral in question is

    [tex]\int e^\frac{-(x-\mu)^2}{(2\sigma)^2}[/tex]

    where [tex]\mu[/tex] and [tex]\sigma[/tex] are constants.

    its part of the normal equation and ive been trying to write a program to do some calculations with it.
  2. jcsd
  3. Nov 24, 2004 #2


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    The integral can be expressed in terms of the error function, erf(x). Unfortunately, there is no elementary form.
  4. Nov 24, 2004 #3


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    As far as I can see, by setting [itex]y = x-\mu /2\sigma[/itex], we get the famous [itex]e^{-y^2}[/itex] which doesn't have a primitive. You can however develop [itex]e^{-y^2}[/itex] as a Taylor serie and integrate term by term. You get the (convergant) serie of general term

    [tex]a_n=\frac{(-1)^n x^{2n+1}}{(2n + 1)n!}[/tex]
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