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

Abstract

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.