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Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function.

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Bibliographic Details
Title: Elegant proofs for properties of normalized remainders of Maclaurin power series expansion of exponential function.
Authors: Li, Yue-Wu1 (AUTHOR) yuewul@126.com, Qi, Feng2 (AUTHOR) qifeng618@gmail.com
Source: Mathematica Slovaca. Oct2025, Vol. 75 Issue 5, p1035-1044. 10p.
Subject Terms: *EXPONENTIAL functions, *MONOTONIC functions, *MATHEMATICAL inequalities, *LOGARITHMS, *POWER series, *INTEGRALS, *MATHEMATICAL proofs
Abstract: In the paper, by establishing an integral representation of a specific Maclaurin power series and in light of two monotonicity rules, the authors present very elegant proofs for several basic properties, including the positivity, (absolute) monotonicity, logarithmic convexity, and inequalities, of the normalized remainders of the Maclaurin power series expansion of the exponential function. [ABSTRACT FROM AUTHOR]
Database: Academic Search Index
Description
Abstract:In the paper, by establishing an integral representation of a specific Maclaurin power series and in light of two monotonicity rules, the authors present very elegant proofs for several basic properties, including the positivity, (absolute) monotonicity, logarithmic convexity, and inequalities, of the normalized remainders of the Maclaurin power series expansion of the exponential function. [ABSTRACT FROM AUTHOR]
ISSN:01399918
DOI:10.1515/ms-2025-0076