Upper bounds for Erd\'elyi's multivariate Laguerre polynomials
Abstract
We establish in this paper two inequalities for the multivariate Laguerre polynomials introduced and studied by Arthur Erd\'elyi [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 Ln(α)(x). We also mention briefly few insightful remarks giving a comparative analysis concerning the upper bounds of the derived inequalities in the concluding section.
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