Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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)?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook