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

2025/01/22 by Achariya Nilsrakoo, Nilsrakoo, Achariya, Weerayuth Nilsrakoo +1
Mathematics · Physics and Astronomy · #11B37 #11B39 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2501.12577

openalex publication_date 2025/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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