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Can we give a meaning to this integral

  1. Apr 15, 2008 #1
    Let be the integral

    [tex] g(x)= \int_{-\infty}^{\infty}dy \frac{f(y)}{ |x-y|^{1/2}} [/tex]

    for given values of 'x' does it mean anything ? , let's take into account that no matter what value of 'x' we chose there is always a singularity at y=x so the expression above would be always divergent , here |x| means absolute value of x or the modulus (in case x is a complex number)
     
  2. jcsd
  3. Apr 15, 2008 #2
    You can understand it as a Cauchy Principal Value integral, which is possibly infinite.
     
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