On the Summation of Series Involving Bessel or Struve Functions

Abstract

The subject called "summation of series" can be viewed in two different ways. From one point of view, it means numerical summation which involves acceleration of convergence, and from the other, it represents a variety of summation formulas which are considered important, but which are often not useful. The aim of this paper is to produce a compromise between the two opposite approaches when series of Bessel or Struve functions are considered. The proposed method leads to series of Riemann zeta and related functions which converge much faster than the originals. In the most significant cases, closed-form formulas were obtained.