Quantum algebras, q-polynomials of Kravchuk and q-functions of Kravchuk-Meixner - Groza , V. A. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
Addition and multiplication theorems are proved for Kravchuk q-polynomials by means of methods from the theory of representations of the quantum algebras $U_q (su_2)$ and $U_q(su_{1,1})$, and Kravchuk-Meixner $q$-functions are introduced and are shown to be orthogonal on the set of integers.