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 | Abstract: | 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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