A symmetric sequence of orthogonal polynomials associated with the Stieltjes–Wigert polynomials

摘要

The Stieltjes–Wigert polynomials are orthogonal with respect to the weight function x(λ ln x) on [0, ∞). In this paper, first we show that using an appropriate shift one can extend the mentioned polynomials to a larger class whose weight function is as x(a+b ln x) on [0, ∞). Then, by using the orthogonality relation of the latter class, we introduce a symmetric sequence of polynomials orthogonal with respect to the weight function ∣x∣(c+d ln ∣x∣) on (−∞, ∞), which is the main purpose of the paper.