The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (154 KB) | Abstract as PDF | Metadata | Table of Contents | ZAA summary
Volume 25, Issue 3, 2006, pp. 393–406
DOI: 10.4171/ZAA/1296

Published online: 2006-09-30

On the Summation of Series in Terms of Bessel Functions

Slobodan B. Trickovic[1], Mirjana V. Vidanovic[2] and Miomir S. Stankovic[3]

(1) University of Nis, Serbia
(2) University of Nis, Serbia
(3) University of Nis, Serbia

In this article we deal with summation formulas for the series %(\ref{1}), $ \sum_{n=1}^\infty\frac{J_\mu(nx)}{n^\nu}\,, $ referring partly to some results from our paper in %\cite{jmaa}. J. Math. Anal. Appl. 247 (2000) 15 -- 26. We show how these formulas arise from different representations of Bessel functions. In other words, we first apply Poisson's or Bessel'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 the limit have been thoroughly analyzed.

Keywords: Bessel functions, Riemann $\z$-function, Poisson formula, Fourier transform

Trickovic Slobodan, Vidanovic Mirjana, Stankovic Miomir: On the Summation of Series in Terms of Bessel Functions. Z. Anal. Anwend. 25 (2006), 393-406. doi: 10.4171/ZAA/1296