Two Forms for Maclaurin Power Series Expansion of Logarithmic Expression Involving Tangent Function-Reference-Cited by-同舟云学术

Two Forms for Maclaurin Power Series Expansion of Logarithmic Expression Involving Tangent Function

Published:2023-09-01 Issue:9 Volume:15 Page:1686
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Li Yue-Wu¹^ORCID,Qi Feng¹²³^ORCID,Du Wei-Shih⁴^ORCID

Affiliation:

1. School of Mathematics and Physics, Hulunbuir University, Inner Mongolia, Hulunbuir 021008, China

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

3. Independent Researcher, Dallas, TX 75252-8024, USA

4. Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan

Abstract

In view of a general formula for higher order derivatives of the ratio of two differentiable functions, the authors establish the first form for the Maclaurin power series expansion of a logarithmic expression in term of determinants of special Hessenberg matrices whose elements involve the Bernoulli numbers. On the other hand, for comparison, the authors recite and revise the second form for the Maclaurin power series expansion of the logarithmic expression in terms of the Bessel zeta functions and the Bernoulli numbers.

Funder

Doctors Foundation of Hulunbuir University

National Science and Technology Council of the Republic of China

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2073-8994/15/9/1686/pdf

Reference33 articles.

1. Gradshteyn, I.S., and Ryzhik, I.M. (2015). Table of Integrals, Series, and Products, Elsevier/Academic Press. Translated from the Russian, Translation edited and with a preface by Daniel Zwillinger and Victor Moll, Eighth edition, Revised from the seventh edition.

2. Power expansions of powers of trigonometric functions and series containing Bernoulli and Euler polynomials;Brychkov;Integral Transform. Spec. Funct.,2009

3. Temme, N.M. (1996). Special Functions: An Introduction to Classical Functions of Mathematical Physics, John Wiley & Sons, Inc.. A Wiley-Interscience Publication.

4. Closed forms: What they are and why we care;Borwein;Not. Am. Math. Soc.,2013

5. Serre, D. (2002). Matrices, Theory and Applications, Springer. Graduate Texts in Mathematics 216; Translated from the 2001 French original.

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