Charlier polynomials - Alchetron, The Free Social Encyclopedia

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

C n ( x ; μ ) = 2 F 0 ( − n , − x , − 1 / μ ) = ( − 1 ) n n ! L n ( − 1 − x ) ( − 1 μ ) ,

where L are Laguerre polynomials. They satisfy the orthogonality relation

∑ x = 0 ∞ μ x x ! C n ( x ; μ ) C m ( x ; μ ) = μ − n e μ n ! δ n m , μ > 0.

References

Charlier polynomials Wikipedia

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