Non-Newtonian Pell and Pell-Lucas numbers

Authors : Tülay Yağmur

Pages : 22-35

Doi:10.54187/jnrs.1447678

View : 95 | Download : 117

Publication Date : 2024-04-30

Article Type : Research

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