Quantum calculus approach to the dual bicomplex Fibonacci and Lucas numbers. (English) Zbl 1513.11048
Summary: Quantum calculus, which arises in the mathematical fields of combinatorics and special functions as well as in a number of areas, involving the study of fractals and multi-fractal measures, and expressions for the entropy of chaotic dynamical systems, has attracted the attention of many researchers in recent years. In this paper, by virtue of some useful notations from \(q\)-calculus, we define the \(q\)-Fibonacci dual bicomplex numbers and \(q\)-Lucas dual bicomplex numbers with a different perspective. Afterwards, we give the Binet formulas, binomial sums, exponential generating functions, Catalan identities, Cassini identities, d’Ocagne identities and some algebraic properties for the \(q\)-Fibonacci dual bicomplex numbers and \(q\)-Lucas dual bicomplex numbers.
MSC:
| 11B39 | Fibonacci and Lucas numbers and polynomials and generalizations |
| 05A15 | Exact enumeration problems, generating functions |
Keywords:
\(q\)-calculus; dual bicomplex numbers; \(q\)-Fibonacci dual bicomplex numbers; \(q\)-Lucas dual bicomplex numbersReferences:
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