Authors: Stanković, Miomir 
Vidanović, Mirjana
Tričković, Slobodan
Title: Summation of some trigonometric and Schlömilch series
Journal: Journal of Computational Analysis and Applications
Volume: 5
Issue: 3
First page: 313
Last page: 331
Issue Date: 1-Jan-2003
Rank: M23
ISSN: 1521-1398
DOI: 10.1023/A:1023275621488
Abstract: 
In this paper we consider trigonometric series in terms of the Riemann zeta function and related functions of reciprocal powers. The obtained closed form formulas we apply to the evaluation of the Riemann zeta function and related functions of reciprocal powers. One can establish recursive relations for them and relations between any two of those functions. These closed formulas enable us also to find sums of some Schlömilch series. We give an example which shows how the convergence of a trigonometric series can be accelerated by applying Krylov's method and our formula (7).
Keywords: Bessel functions | Riemann zeta and related functions
Publisher: Springer Link

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