Authors: Tričković, Slobodan
Vidanović, Mirjana
Stanković, Miomir 
Title: On the summation of series over a product of Bessel functions
Journal: Integral Transforms and Special Functions
Volume: 17
Issue: 10
First page: 749
Last page: 758
Issue Date: 1-Oct-2006
Rank: M23
ISSN: 1065-2469
DOI: 10.1080/10652460600856351
In this article, we deal with summation formulas for the series (3), referring partly to some results from our article [Stanković, M.S., Vidanović, M.V. and Tričković, S.B., 2000, On the summation of series in involving Bessel or Struve functions. Journal of Mathematics and Analytical Applications, 247, 15-26]. We show how these formulas arise from different representations of Bessel functions. In other words, we first apply Gegenbauer'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 limit have been thoroughly analyzed.
Keywords: Bessel functions | Fourier transform | Poisson's formula | Riemann's ζ function
Publisher: Taylor & Francis

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