The homogeneous little q$q$‐Jacobi polynomials

Abstract Motivated by the ‐operational equation for Rogers–Szegö polynomials [Sci. China Math. 66 (2023), no. 6, 1199–1216], it is natural to ask whether some general ‐polynomials exist, which are solutions of certain ‐operational equations, ‐difference equations, and ‐partial differential equations. In this paper, based on the importance of little ‐Jacobi polynomials, we define two homogeneous little ‐Jacobi polynomials and search their corresponding ‐operational equations, ‐difference equations, and ‐partial differential equations by the technique of noncommutative ‐binomial theorem and recurrence relations. In addition, we deduce some generating functions for homogeneous little ‐Jacobi polynomials by methods of ‐operational equation, ‐difference equation, and ‐partial differential equation. Moreover, we consider recurrence relations for homogeneous little ‐Jacobi polynomials.