Quantum algebras, Kravchuk \(q\)-polynomials, and Kravchuk-Meixner \(q\)-function (Q1206311)

The author proves the theorems of addition and of multiplication for the Kravchuk \(q\)-polynomials by means of the methods coming from the theory of representations of quantum algebra \(U_ q(su_ 2)\) and \(U_ q(su_{1,1})\). He uses the relation between the \(q\)-hypergeometric functions and the \(q\)-orthogonal polynomials. The Kravchuk-Meixner \(q\)- functions are also introduced and the proof of their orthogonality on the set of integers is achieved.