Bo, Rui; Wong, R. Uniform asymptotic expansion of Charlier polynomials. (English) Zbl 0846.41025 Methods Appl. Anal. 1, No. 3, 294-313 (1994). Summary: The Charlier polynomials \(C_n^{(a)} (x)\) form an orthogonal system on the positive real line \(x>0\) with respect to the distribution \(d\alpha (x)\), where \(\alpha (x)\) 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 \(C_n^{(a)} (n\beta)\), as \(n\to \infty\), which holds uniformly for \(0< \varepsilon\leq \beta\leq M< \infty\). Our result includes as special cases all seven asymptotic formuals recently given by W. M. Y. Goh. Cited in 20 Documents MSC: 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) Keywords:Charlier polynomials PDFBibTeX XMLCite \textit{R. Bo} and \textit{R. Wong}, Methods Appl. Anal. 1, No. 3, 294--313 (1994; Zbl 0846.41025) Full Text: DOI Digital Library of Mathematical Functions: Charlier ‣ §18.24 Hahn Class: Asymptotic Approximations ‣ Askey Scheme ‣ Chapter 18 Orthogonal Polynomials