On trigonometric series over integrals involving Bessel or Struve functions

Abstract

To find formulas for the summation of trigonometric series over integrals involving Bessel or Struve functions, we rely on trigonometric series involving Bessel or Struve functions, which are in turn obtained by using summation formulas for series over the product of two trigonometric functions. All these sums are expressed either as power series in terms of Riemann's ζ or Catalan's β function or Dirichlet functions η and λ, or, in certain cases, they are brought in so called closed form, which means that the infinite series are represented by finite sums. Important limiting values cases are considered too. © 2009 Taylor & Francis.