Integral Representations of Generalizations of Pell Num-bers and their Companion Numbers

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.