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On Qi’s Normalized Remainder of Maclaurin Power Series Expansion of Logarithm of Secant Function

Authors :
Hong-Chao Zhang
Bai-Ni Guo
Wei-Shih Du
Source :
Axioms, Vol 13, Iss 12, p 860 (2024)
Publication Year :
2024
Publisher :
MDPI AG, 2024.

Abstract

In the study, the authors introduce Qi’s normalized remainder of the Maclaurin power series expansion of the function lnsecx=−lncosx; in view of a monotonicity rule for the ratio of two Maclaurin power series and by virtue of the logarithmic convexity of the function (2x−1)ζ(x) on (1,∞), they prove the logarithmic convexity of Qi’s normalized remainder; with the aid of a monotonicity rule for the ratio of two Maclaurin power series, the authors present the monotonic property of the ratio between two Qi’s normalized remainders.

Details

Language :
English
ISSN :
20751680
Volume :
13
Issue :
12
Database :
Directory of Open Access Journals
Journal :
Axioms
Publication Type :
Academic Journal
Accession number :
edsdoj.1cd686565aeb4668879db72c4b8a31d7
Document Type :
article
Full Text :
https://doi.org/10.3390/axioms13120860