Integral Representations of Generalizations of Pell Num-bers and their Companion Numbers
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i3.6452Keywords:
Generalized Pell numbers, Generalized Pell-Lucas-like numbers, Integral representationAbstract
This paper discusses a one-parameter generalization of Pell numbers that preserves the recurrence relation with arbitrary initial conditions. We introduce generalized Pell-Lucas-like numbers, which are simple associations of generalized Pell numbers. Consequently, we give some new and well-known identities. Furthermore, we propose integral representations of these numbers associated with generalized Pell and Pell-Lucas-like numbers. Our results not only generalize the integral representations of the Pell and Pell-Lucas numbers but also apply to all companion numbers of generalized Pell numbers.
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Copyright (c) 2025 Weerayuth Nilsrakoo, Achariya Nilsrakoo
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