We give a formula for the density of the free convolution of an arbitrary probability measure with a semi-circular distribution. We use this formula to establish a certain number of regularity ...

Besge presented the result about the convolution sum of divisor functions. Since then Liouville obtained the generalized version of Besge’s formula, which is the binomial convolution sum of divisor ...

In a lecture example, we used the convolution integral approach to study the response of an undamped oscillator excited by the rectangular pulse shown below. Here we will apply the graphical ...