Uniform asymptotic expansion of Charlier polynomials

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)294-313
Journal / PublicationMethods and Applications of Analysis
Issue number3
Publication statusPublished - 1994
Externally publishedYes


The Charlier polynomials Cn (x) form an orthogonal system on the positive real line x > 0 with respect to the distribution da(x), where a(x) is a step function with jumps at the non-negative integers. Unlike classical orthogonal polynomials, they do not satisfy a second-order linear differential equation. An infinite asymptotic expansion is derived for C^ (nfi), as n —► oo, which holds uniformly for 0<£</3<M<oo. Our result includes as special cases all seven asymptotic formulas recently given by W. M. Y. Goh.