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A new class of sum rules for products of Bessel functions. (English) Zbl 1315.33009

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}

MSC:

33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
76X05 Ionized gas flow in electromagnetic fields; plasmic flow

Citations:

Zbl 0509.76117
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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
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