On constructing distribution functions: With applications to Lommel polynomials and Bessel functions

Abstract

where the polynomials On(x) are recursively defined by: - 1(x) = 0, O(x) = 1, and (I-A) n+ (x) = (x - anX)-(x) - bnn- i(X) (n > 0). This study begins by showing how to obtain such a function +(x) for certain classes of sequences {an}l and {bn}l . Then we apply our results to obtain a distribution function for the modified Lommel polynomials (thus answering a question of Dickinson, [10, p. 121]) and to obtain some information about Bessel functions as a function of their order.