A class of orthogonal polynomials of a new type

Abstract

The purpose of this paper is to study a class of polynomials Fnm(x,λ,ν) associated with a class of m differential equations, where λ is fixed, n is a variable parameter, m is fixed positive integer and ν is a non-negative integer <m. We also obtain all the important properties of this class of polynomials including Rodrigues' formulas, generating function, and recurrence relations. Several special cases of interest are obtained from our analysis.

Keywords

• function space
• weight function
• generating function
• and recurrence relation.