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arXiv · 2507.11024

Upper bounds for Erd\'{e}lyi's multivariate Laguerre polynomials

Min-Jie Luo·Ravinder Krishna Raina
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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 $L_n^{(\alpha)}(x)$. 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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Min-Jie Luo, Ravinder Krishna Raina. 2025-07-15. Upper bounds for Erd\'{e}lyi's multivariate Laguerre polynomials. https://arxiv.org/abs/2507.11024

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