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.