Charlier polynomials are a sequence of orthogonal polynomials that arise in probability and analysis. They are a specific case of hypergeometric polynomials and can be defined in the context of the Poisson distribution. The Charlier polynomials \( C_n(x; a) \) are defined as follows: \[ C_n(x; a) = \sum_{k=0}^{n} \frac{(-1)^{n-k}}{(n-k)!
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