Further results on generalized Kapteyn-type expansions

doi:10.1016/j.aml.2008.03.008

Applied Mathematics Letters

Volume 22, Issue 2, February 2009, Pages 192-196

In memoriam Csörgő Sándor, dear friend and great scholar

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Abstract

A new inequality is derived for the Bessel function of the first kind $J_{ν} (z), ν \in R$ , and a discussion of the consequent convergence is given for the generalized Kapteyn-type expansion, improving certain results obtained recently by the author.

Keywords

Bessel function of first kind

J_{ν} (z)

Bounds for

J_{ν} (z)

Positive zeros

j_{ν, s}

J_{ν} (z)

Generalized Kapteyn expansion

Kapteyn series