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Integral, possible ?

  1. Dec 10, 2008 #1

    I have an integral that I find quite difficult, I can't obtain anything from mathematica (but I'm far from being an expert).

    Would some of you have a hint ? is it analytical ? It seems to be a "simple" function, from the physicist I am it should be integrable...

    this integral is :

    [tex]\int_{-\infty}^{+\infty}Exp(-x^2)*Erf(x^2 - a^2)dx[/tex]

    Thanks !
  2. jcsd
  3. Dec 10, 2008 #2


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    Mathematica doesn't give me an analytical solution either.
    But the integrand seems to be sharply peaked around x = 0, and we have the nice result
    [tex]\frac{d}{dx} \operatorname{erf}(x) = \frac{2}{\sqrt{\pi}} e^{-x^2}[/tex]
    so maybe you can do something like steepest descent (expand the integrand around 0)?
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