Moments and (p; q)-Integral Representations of (p; q)-Classical Forms
Keywords:
(p; q) calculus; (p; q)-di erence operator; (p; q)-classical polynomialAbstract
In [6], the authors introduce a new technical method for studying the Dp,q-classical orthogonal polynomials, where Dp,q is the(p,q)-difference operator, using an algebraic approach. In this paper, we investigate Dp,q-classical orthogonal polynomials associated with the(p,q)-difference op-eratorDp,q. Using Pearson-type functional equations and a suitable de-composition of Dp,q, we simplify the description of the canonical Dp,q-classical forms and clarify their relation with theq-classical framework.We also study the moments and modified moments of the correspondingforms, derive recurrence relations, and establish several explicit (p,q)-integral representations for canonical cases
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Copyright (c) 2026 Mabrouk Sghaier, Mohamed Zaatra
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