Increasing property and logarithmic convexity of functions involving Dirichlet lambda function-Reference-Cited by-同舟云学术

Increasing property and logarithmic convexity of functions involving Dirichlet lambda function

Published:2023-01-01 Issue:1 Volume:56 Page:
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Qi Feng¹²,Lim Dongkyu³

Affiliation:

1. Institute of Mathematics, Henan Polytechnic University , Jiaozuo 454010 , Henan , China

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

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

Abstract

Abstract In this article, with the help of an integral representation of the Dirichlet lambda function, by means of a monotonicity rule for the ratio of two integrals with a parameter, and by virtue of complete monotonicity and another property of an elementary function involving the exponential function, the authors find increasing property and logarithmic convexity of two functions containing the gamma function and the Dirichlet lambda function.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2022-0243/pdf

Reference29 articles.

1. D. S. Bernstein, Scalar, Vector, and Matrix Mathematics: Theory, Facts, and Formulas, Revised and expanded edition, Princeton University Press, Princeton, NJ, 2018.

2. N. M. Temme, Special Functions: An Introduction to Classical Functions of Mathematical Physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, DOI: https://doi.org/10.1002/9781118032572.

3. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, Translated from the Russian, Translation edited and with a preface by Daniel Zwillinger and Victor Moll, Eighth edition, Revised from the seventh edition, Elsevier/Academic Press, Amsterdam, 2015, DOI: https://doi.org/10.1016/B978-0-12-384933-5.00013-8.

4. F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, New York, 2010, http://dlmf.nist.gov/.

5. M. Abramowitz and I. A. Stegun (Eds), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, vol. 55, 10th Printing, Washington, 1972.

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Expanding the function $\ln(1+\operatorname{e}^x)$ into power series in terms of the Dirichlet eta function and the Stirling numbers of the second kind;Carpathian Mathematical Publications;2024-06-30

2. Several Functions Originating from Fisher–Rao Geometry of Dirichlet Distributions and Involving Polygamma Functions;Mathematics;2023-12-22

3. Norm and Numerical Radius Inequalities Related to the Selberg Operator;Symmetry;2023-10-03