AN INTEGRAL REPRESENTATION OF THE PELL NUMBERS AND THE PELL-LUCAS NUMBERS

DOI: 10.18173/2354-1059.2025-0002

Abstract

We report on an integral representation for the Pell sequence, Pell-Lucas sequence, Balancing sequence and Lucas-Balancing sequence. This integral representation is based on the generating function and the Binet-like formulas of the aforementioned sequences. Many other integral representations of these numbers can be found by applying the other known relations between them.