Charlier polynomials
In mathematics, Charlier polynomials are a family of orthogonal polynomials introduced by Carl Charlier.
They are given in terms of the generalized hypergeometric function by
where 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.