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 . 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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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 8, pp. 1055–1063, August, 1998.
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Kachurik, I.I. q-Numbers of quantum groups, Fibonacci numbers, and orthogonal polynomials. Ukr Math J 50, 1201–1211 (1998). https://doi.org/10.1007/BF02513092
- Orthogonal Polynomial
- Quantum Group
- Chebyshev Polynomial
- Arithmetic Progression
- Summation Formula