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Asymptotic root distribution of Charlier polynomials with large negative parameter
- Publication Year :
- 2022
-
Abstract
- We analyze the asymptotic distribution of roots of Charlier polynomials with negative parameter depending linearly on the index. The roots cluster on curves in the complex plane. We determine implicit equations for these curves and deduce the limiting density of the root distribution supported on these curves. The proof is based on a determination of the limiting Cauchy transform in a specific region and a careful application of the saddle point method. The obtained result represents a solvable example of a more general open problem.<br />Comment: 26 pages
- Subjects :
- Mathematics - Classical Analysis and ODEs
33C45, 26C10, 30C15, 30E15
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2210.16922
- Document Type :
- Working Paper