Asymptotics for the ratio and the zeros of multiple Charlier polynomials

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• 作者：Franç ; ois Ndayiragije ^{francois.ndayiragije@wis.kuleuven.be} ; Walter Van Assche ; ^{walter@wis.kuleuven.be}
• 关键词：Multiple Charlier polynomials ; Ratio asymptotics ; Asymptotic zero distribution ; Recurrence relation
• 刊名：Journal of Approximation Theory
• 出版年：2012
• 期刊代码：71_00219045
• 类别：mt
• 出版时间：June, 2012
• 卷：164
• 期：6
• 页码：823-840
• 文件大小：279 K

摘要

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 depends on the degree of the polynomial, in which case we obtain another asymptotic distribution of the zeros.