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

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.