On the summation of trigonometric series

Abstract

We deal with the series (Equation Presented) and express it as a power series in terms of Riemann's ζ or Catalan's β function or Dirichlet functions η and λ. Also, closed form cases as well as those when it is necessary to take limit have been thoroughly analyzed. Some applications such as convergence acceleration are considered too. © 2008 Taylor & Francis.