Abstract
In this paper, we provide a novel generalization of quantum orthogonal polynomials from [Formula: see text]-deformed quantum algebras introduced in earlier works. We construct related quantum Jacobi polynomials and their probability distribution, factorial moments, recurrence relation, and governing difference equation. Surprisingly, these polynomials obey non-conventional recurrence relations. Particular cases of generalized quantum little Legendre, little Laguerre, Laguerre, Bessel, Rogers–Szegö, Stieltjes–Wigert and Kemp binomial polynomials are derived and discussed.
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