On the Proof of an Inequality Related to the Mathieu Series

Dejun Zhao

doi:https://doi.org/10.14445/22315373/IJMTT-V67I10P507

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 10 | Year 2021 | Article Id. IJMTT-V67I10P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I10P507

On the Proof of an Inequality Related to the Mathieu Series

Dejun Zhao

Abstract

In this paper, we first show that there is a mistake in the proof of an inequality related to the Mathieu series which given by J. Ernest Wilkins Jr., but his proof method is still valuable and can be modified. Follow this method we have improved the corresponding proof process in the last section.

Keywords

Mathieu series, Alzer-Brenner-Ruehr’s inequality, the trigamma function, Riemann Zeta function.

References

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Citation :

Dejun Zhao, "On the Proof of an Inequality Related to the Mathieu Series," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 10, pp. 72-76, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I10P507