THE LAGUERRE TYPE POLYNOMIALS ORTHOGONAL WITH VARYING WEIGHT

Abstract

The standard theory of orthogonal polynomials understand the weight function like a positive function on a support depending only on the variable. Occasionally, some fixed parameters are present. But, a few researchers in the theoretical physics, showed that eigenfunctions of a differential equation can be the polynomials orthogonal with respect to the weight function which depends on their degrees. Here, we will generalize these considerations and offer procedures for finding any arbitrary sequence member. Especially, our attention occupies a Laguerre case which we successfully examined.