Summations of Schlömilch series containing modified Bessel function of the second kind terms

Abstract

The main aim of this article is to establish certain closed expressions for the Schlömilch series which members contain modified Bessel functions of the second kind and to obtain connection between special case of such series and a generalized Mathieu series. Closed expressions for the Schlömilch series with members containing products of and modified Bessel function of the first kind are derived as a by-product of these results.

Keywords:

• Schlömilch series
• modified Bessel function of the second kind
• summation formulas

AMS Subject Classification:

• Primary: 33C10
• 11B68
• Secondary: 40C10
• 65B10

Acknowledgments

The author wishes to thank Tibor K. Pogány for his very kind and continuous help in preparing, improving and finishing the manuscript of this article.

Funding

The research of D. Jankov Maširević was supported by the Croatian Science Foundation under Project 5435.