On the summation of series over a product of Bessel functions

Abstract

In this article, we deal with summation formulas for the series (3), referring partly to some results from our article [Stanković, M.S., Vidanović, M.V. and Tričković, S.B., 2000, On the summation of series in involving Bessel or Struve functions. Journal of Mathematics and Analytical Applications, 247, 15-26]. We show how these formulas arise from different representations of Bessel functions. In other words, we first apply Gegenbauer's integral, then in the sequel we define a function by means of the power series representation of Bessel functions and make use of Poisson's formula. Also, closed-form cases as well as those when it is necessary to take limit have been thoroughly analyzed.