Generalization of the electrostatic potential function for an infinite charge distribution

The asymptotic conditions needed to define the electrostatic potential due to an infinite charge distribution are studied in detail. It is shown that if the charge distribution decreases faster than the square of the distance when |r| goes to infinity, the convolution integral defining the potential exists, goes to zero as |r| goes to infinity, and therefore allows the calculation of the electric potential function at any point in space, even if the total charge is infinite. We illustrate the calculation of the electric potential with a simple example of a spherically symmetric infinite charge distribution.