$q$-Numbers of quantum groups, Fibonacci numbers, and orthogonal polynomials

• Date: 1998
• Main Authors: Kachurik, I. I., Качурик, І. І.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1998
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4854
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We obtain algebraic relations (identities) for $q$-numbers that do not contain $q^{α}$-factors. We derive a formula that expresses any $q$-number $[x]$ in terms of the $q$-number [2]. We establish the relationship between the $q$-numbers $[n]$ and the Fibonacci numbers, Chebyshev polynomials, and ot...