An Integral Representation of the Generalized Fibonacci Numbers
arXiv:2609.25106 · doi:10.1080/00150517.2025.2540644
Abstract
In this note, we present an integral representation of the -generalized Fibonacci sequence and provide a proof using contour integration. This representation enables the derivation of several known identities and a Binet-type formula related to the -generalized Fibonacci sequence.