In mathematics, Charlier polynomials (also called Poisson–Charlier polynomials) are a family of orthogonal polynomials introduced by Carl Charlier. They are given in terms of the generalized hypergeometric function by

where ${\displaystyle L}$ are generalized Laguerre polynomials. They satisfy the orthogonality relation

They form a Sheffer sequence related to the Poisson process, similar to how Hermite polynomials relate to the Brownian motion.