Bevilacqua, G.; Biancalana, V.; Dancheva, Y.; Mansour, T.; Moi, L. A new class of sum rules for products of Bessel functions. (English) Zbl 1315.33009 J. Math. Phys. 52, No. 3, 033508, 9 p. (2011). Summary: We derive a new class of sum rules for products of Bessel functions of the first kind. Using standard algebraic manipulations we extend some of the well known properties of \(J_{n}\). Some physical applications of the results are also discussed. A comparison with the Newberger [B. S. Newberger, ibid. 23, 1278–1281 (1982; Zbl 0509.76117)] sum rules is performed on a typical example.{©2011 American Institute of Physics} Cited in 1 Document MSC: 33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\) 76X05 Ionized gas flow in electromagnetic fields; plasmic flow Citations:Zbl 0509.76117 PDFBibTeX XMLCite \textit{G. Bevilacqua} et al., J. Math. Phys. 52, No. 3, 033508, 9 p. (2011; Zbl 1315.33009) Full Text: DOI arXiv References: [1] Gray, A.; Mathews, G. B., A Treatise on Bessel Functions and their Applications to Physics (1895) · JFM 25.0836.01 [2] Watson, G. N., A Treatise on the Theory of Bessel Functions (1922) · JFM 48.0412.02 [3] Korenev, B. G., Bessel Functions and their Applications (2002) · Zbl 1065.33001 [4] Dattoli, G.; Torre, A., Theory and Applications of Generalized Bessel Functions (1996) [5] Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (1964) · Zbl 0171.38503 [6] Newberger, B. S., J. Math. Phys., 23, 1278 (1982) · Zbl 0509.76117 · doi:10.1063/1.525510 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.