On the Integral Representations of the $k$-Pell and $k$-Pell-Lucas Numbers
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913920345702400 |
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| author | Nilsrakoo, Achariya Nilsrakoo, Weerayuth |
| author_facet | Nilsrakoo, Achariya Nilsrakoo, Weerayuth |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_12577 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Integral Representations of the $k$-Pell and $k$-Pell-Lucas Numbers Nilsrakoo, Achariya Nilsrakoo, Weerayuth Number Theory 11B39, 11B37 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. |
| title | On the Integral Representations of the $k$-Pell and $k$-Pell-Lucas Numbers |
| topic | Number Theory 11B39, 11B37 |
| url | https://arxiv.org/abs/2501.12577 |