The asymptotic zero distribution of Lommel polynomials as polynomials of the order with a variable complex argument
Classical Analysis and ODEs
2021-02-02 v2
Abstract
We study the asymptotic distribution of roots of Lommel polynomials as polynomials of the order with a variable and purely imaginary argument. The roots are complex and accumulate on certain curves in the complex plane. We prove existence of the weak limit of corresponding root-counting measures and deduce formulas for the supporting curves and density. The obtained result represents a solvable example of a more general problem which is still open. Numerical illustrations of the main result are also involved.
Keywords
Cite
@article{arxiv.1910.02271,
title = {The asymptotic zero distribution of Lommel polynomials as polynomials of the order with a variable complex argument},
author = {Petr Blaschke and František Štampach},
journal= {arXiv preprint arXiv:1910.02271},
year = {2021}
}
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