On the solutions of some integral equations involving generating functions

It is well-known that one of the important applications of the Hermite polynomials is that they constitute solutions of the simple harmonic oscillator of quantum mechanics. An important method for solving problems from applications involves the use of generating functions. It is also known that Fredholm integral equations arise in many different branches of science. Interest in solving them analytically or numerically has been growing recently. In this study, we aim to introduce a method to solve a set of singular integral equations, usually considered as an ill-posed problem, whose kernel involve the generating function for Hermite polynomials.