On the Integral Representations of the $k$-Pell and $k$-Pell-Lucas Numbers

Achariya Nilsrakoo; Weerayuth Nilsrakoo

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arXiv · 2501.12577

On the Integral Representations of the $k$-Pell and $k$-Pell-Lucas Numbers

Achariya Nilsrakoo·Weerayuth Nilsrakoo

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Abstract

In this paper, the integral representations of the $k$-Pell and $k$-Pell-Lucas numbers are presented. Using Binet's formulas for these numbers, we obtain a number of identities and use elementary integral calculus to confirm their integral representations.Our results are also deduced and related to the Fibonacci, Lucas, Pell, and Pell-Lucas numbers.

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Achariya Nilsrakoo, Weerayuth Nilsrakoo. 2025-01-22. On the Integral Representations of the $k$-Pell and $k$-Pell-Lucas Numbers. https://arxiv.org/abs/2501.12577

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