Non-Newtonian Pell and Pell-Lucas numbers

Year 2024, Volume: 13 Issue: 1, 22 - 35, 30.04.2024

Tülay Yağmur

https://doi.org/10.54187/jnrs.1447678

Abstract

In the present paper, we introduce a new type of Pell and Pell-Lucas numbers in terms of non-Newtonian calculus, which we call non-Newtonian Pell and non-Newtonian Pell-Lucas numbers, respectively. In non-Newtonian calculus, we study some significant identities and formulas for classical Pell and Pell-Lucas numbers. Therefore, we derive some relations with non-Newtonian Pell and Pell-Lucas numbers. Furthermore, we investigate some properties of non-Newtonian Pell and Pell-Lucas numbers, including Catalan-like identities, Cassini-like identities, Binet-like formulas, and generating functions.

Keywords

Non-Newtonian calculus, Pell number, Pell-Lucas number

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