The Inversion of an Integral Equation Involving a General Class of Polynomials

The object of the present paper is to derive the solution of a certain convolution integral equation of Fredholm type whose kernel involves a generalization of numerous polynomial systems including, for example, the classical Hermite, Laguerre, and Bessel polynomials, and the Konhauser biorthogonal polynomials. Some interesting applications of the main inversion theorem are also mentioned. One of these applications is shown to lead to the correct solutions of certain integral equations which were considered recently