Quantum algebras, q-polynomials of Kravchuk and q-functions of Kravchuk-Meixner

• Date: 1992
• Main Authors: Groza , V. A., Гроза , В. А.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 1992
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/8130
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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.