$q$-Numbers of quantum groups, Fibonacci numbers, and orthogonal polynomials
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...
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| Date: | 1998 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1998
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4854 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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 other special functions. The sums of combinations of $q$-numbers, in particular, the sums of their powers, are calculated. Linear and bilinear generating functions are found for “natural” $q$-numbers. |
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