On Generalized Pell Numbers of Order r ≥ 2
DOI:
https://doi.org/10.5540/tcam.2021.022.01.00125Keywords:
Generalized Pell fundamental system, Generalized Pell numbers, Combinatorial identities, Analytic representations, Generalized Cassini identityAbstract
In this paper we investigate the generalized Pell numbers of order r ≥ 2 through the properties of their related fundamental system of generalized Pell numbers. That is, the generalized Pell number of order r ≥ 2; are expressed as a linear combination of a fundamental system of generalized Pell numbers. The properties of this fundamental system are examined and results can be established for generalized Pell numbers of order r ≥ 2. Some identities and combinatorial results are established. Moreover, the analytic study of the fundamental system of generalized Pell is provided. Furthermore, the generalized Pell Cassini identity type is provided.
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