Extended q-Jacobi polynomial and its properties

Abstract

In this paper, we define an extended \( \textit{q} \)-Jacobi polynomial using the Wright-type \( \textit{q} \)-hypergeometric function and discuss its analytical properties, including recurrence and contiguous relations, integral and derivative formulas, as well as integral representations. Also, integral transforms, such as the Laplace, Sumudu, and Natural transforms have been derived.