Asymptotics for the ratio and the zeros of multiple Charlier polynomials

Details Asymptotics for the ratio and the zeros of multiple Charlier polynomials Asymptotics for the ratio and the zeros of multiple Charlier polynomials

2011-08-19

arxiv.org/abs/1108.3918v1

Mathematics

Classical Analysis and ODEs

19 pages, 3 figures

Scientific paper

We investigate multiple Charlier polynomials and in particular we will use the (nearest neighbor) recurrence relation to find the asymptotic behavior of the ratio of two multiple Charlier polynomials. This result is then used to obtain the asymptotic distribution of the zeros, which is uniform on an interval. We also deal with the case where one of the parameters of the various Poisson distributions depend on the degree of the polynomial, in which case we obtain another asymptotic distribution of the zeros.

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