Power series expansion, decreasing property, and concavity related to logarithm of normalized tail of power series expansion of cosine-Reference-Cited by-同舟云学术

Power series expansion, decreasing property, and concavity related to logarithm of normalized tail of power series expansion of cosine

Published:2024 Issue:5 Volume:32 Page:3130-3144
ISSN:2688-1594
Container-title:Electronic Research Archive
language:
Short-container-title:era

Author:

Wan Aying¹,Qi Feng¹²³

Affiliation:

1. Department of Science and Technology, Hulunbuir University, Hulunbuir 021008, China

2. School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo 454010, China

3. Independent researcher, University Village, Dallas 75252, USA

Abstract

<abstract><p>In this paper, in view of a determinantal formula for higher order derivatives of the ratio of two differentiable functions, we expand the logarithm of the normalized tail of the power series expansion of the cosine function into a Maclaurin power series expansion whose coefficients are expressed in terms of specific Hessenberg determinants, present the decreasing property and concavity of the normalized tail of the Maclaurin power series expansion of the cosine function, deduce a new determinantal expression of the Bernoulli numbers, and verify the decreasing property for the ratio of the logarithms of the first two normalized tails of the Maclaurin power series expansion of the cosine function.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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