Work

Decreasing ratio between two normalized remainders of Maclaurin series expansion of exponential function

Year: 2025

Type: article

Abstract: In the study, the authors concisely review the normalized remainders of the Maclaurin series and, by establishing an inequality for specific Maclaurin series, show that the ratio between two normalized remainders of the Maclaurin series of the exponential function is decreasing on the whole real axis. This decreasing property confirms a guess in Remark 5 of the paper 'F. Qi, Absolute monotonicity of normalized tail of power series expansion of exponential function, Mathematics, 12 (2024), 2859, available online at https://doi.org/10.3390/math12182859'.

Source: AIMS Mathematics

DOI: 10.3934/math.2025663

Authors: Tao Zhang, Feng Qi, Retired researcher, 17709 Sabal Court, Dallas, TX 75252-8024, USA

Institutions: Inner Mongolia Normal University, Hulunbuir University, Henan Polytechnic University

Language: English

Topic: Mathematical Inequalities and Applications

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funders: National Natural Science Foundation of China, Natural Science Foundation of Inner Mongolia