$p$-extended Mathieu series from the Schl\"omilch series point of view

TL;DR

This paper explores the relationship between $p$-extended Mathieu series and Schl"omilch series, providing new insights into their mathematical connections and properties.

Contribution

It establishes a novel link between $p$-extended Mathieu series and various Schl"omilch series, expanding understanding of these special functions.

Findings

Derived new formulas connecting Mathieu and Schl"omilch series

Enhanced understanding of the properties of $p$-extended Mathieu series

Provided potential applications in mathematical analysis

Abstract

Motivated by certain current results by Parmar and Pog\'any [9] in which the authors introduced the so-called $p$-extended Mathieu series the main aim of this paper is to present a connection between such series and a various types of Schl\"omilch series.