Can we give a meaning to this integral

[mhill]

Let be the integral

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

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)

 

[Pere Callahan]

You can understand it as a Cauchy Principal Value integral, which is possibly infinite.