Upper bounds for Erd\'{e}lyi's multivariate Laguerre polynomials
Classical Analysis and ODEs
2025-07-16 v1 Complex Variables
Abstract
We establish in this paper two inequalities for the multivariate Laguerre polynomials introduced and studied by Arthur Erd\'{e}lyi [Sitzungsber. Akad. Wiss. Wien, Math.-Naturw. Kl., Abt. IIa 146 (1937), 431--467]. These inequalities generalize the well-known Szeg\"{o}'s inequality for the Laguerre polynomials . We also mention briefly few insightful remarks giving a comparative analysis concerning the upper bounds of the derived inequalities in the concluding section.
Cite
@article{arxiv.2507.11024,
title = {Upper bounds for Erd\'{e}lyi's multivariate Laguerre polynomials},
author = {Min-Jie Luo and Ravinder Krishna Raina},
journal= {arXiv preprint arXiv:2507.11024},
year = {2025}
}