Authors: Tričković, Slobodan
Vidanović, Mirjana
Stanković, Miomir 
Title: On the summation of series in terms of Bessel functions
Journal: Zeitschrift fur Analysis und ihre Anwendung
Volume: 25
Issue: 3
First page: 393
Last page: 406
Issue Date: 1-Jan-2006
Rank: M23
ISSN: 0232-2064
DOI: 10.4171/ZAA/1296
Abstract: 
In this article we deal with summation formulas for the series Σn=1∞ Jμ(nx)/nv referring partly to some results from our paper in 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 | Fourier's transform | Poisson's formula | Riemann's ζ-function
Publisher: European Mathematical Society

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