Inequalities for the exponential remainder of the Taylor series

2016/08/31 by С. М. Ситник, S. M. Sitnik, Sitnik, S. M.
Mathematics · #26D15 #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematics and Applications #math.CA #msc:26D15

paper · pdf · doi:10.48550/arxiv.1608.08784

33 p., text in Russian, resume, contents and comments on recent papers with updated references are in English

openalex publication_date 2016/08/31 · arxiv created 2016/09/29 · arxiv updated 2016/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a preprint of 1992 with some updates. We study sections of the exponential function Taylor series. Interesting inequalities for these sections were considered by G.Hardy, Kesava Menon, W. Gautschi, H.Alzer and others. The main aim of this preprint is to investigate new proofs for the main inequality with best constants and its multiple generalizations. Some conjectures are formulated (and some of them were proved recently, see comments of 2016).

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