Non-Newtonian Pell and Pell-Lucas numbers

Tülay Yağmur

doi:10.54187/jnrs.1447678

EN

Non-Newtonian Pell and Pell-Lucas numbers

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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Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Authors

Tülay Yağmur ^*
0000-0002-6224-1921
Türkiye

Publication Date

April 30, 2024

Submission Date

March 5, 2024

Acceptance Date

April 26, 2024

Published in Issue

Year 2024 Volume: 13 Number: 1

DOI

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

IZ

https://izlik.org/JA49XT84MP

APA

Yağmur, T. (2024). Non-Newtonian Pell and Pell-Lucas numbers. Journal of New Results in Science, 13(1), 22-35. https://doi.org/10.54187/jnrs.1447678

AMA

1.Yağmur T. Non-Newtonian Pell and Pell-Lucas numbers. JNRS. 2024;13(1):22-35. doi:10.54187/jnrs.1447678

Chicago

Yağmur, Tülay. 2024. “Non-Newtonian Pell and Pell-Lucas Numbers”. Journal of New Results in Science 13 (1): 22-35. https://doi.org/10.54187/jnrs.1447678.

EndNote

Yağmur T (April 1, 2024) Non-Newtonian Pell and Pell-Lucas numbers. Journal of New Results in Science 13 1 22–35.

IEEE

[1]T. Yağmur, “Non-Newtonian Pell and Pell-Lucas numbers”, JNRS, vol. 13, no. 1, pp. 22–35, Apr. 2024, doi: 10.54187/jnrs.1447678.

ISNAD

Yağmur, Tülay. “Non-Newtonian Pell and Pell-Lucas Numbers”. Journal of New Results in Science 13/1 (April 1, 2024): 22-35. https://doi.org/10.54187/jnrs.1447678.

JAMA

1.Yağmur T. Non-Newtonian Pell and Pell-Lucas numbers. JNRS. 2024;13:22–35.

MLA

Yağmur, Tülay. “Non-Newtonian Pell and Pell-Lucas Numbers”. Journal of New Results in Science, vol. 13, no. 1, Apr. 2024, pp. 22-35, doi:10.54187/jnrs.1447678.

Vancouver

1.Tülay Yağmur. Non-Newtonian Pell and Pell-Lucas numbers. JNRS. 2024 Apr. 1;13(1):22-35. doi:10.54187/jnrs.1447678