Upper bounds for Erdélyi's multivariate Laguerre polynomials

Abstract

We establish in this paper two inequalities for the multivariate Laguerre polynomials introduced and studied by Arthur Erdélyi [Sitzungsber. Akad. Wiss. Wien, Math.-Naturw. Kl., Abt. IIa 146 (1937), 431--467]. These inequalities generalize the well-known Szegö's inequality for the Laguerre polynomials $L_n^{(\hat{I}\pm )}(x)$. We also mention briefly few insightful remarks giving a comparative analysis concerning the upper bounds of the derived inequalities in the concluding section.