Sum rule for products of Bessel functions: Comments on a paper by Newberger

Recently, Newberger considered a series of Bessel functions with as a special case the form ∑(njJ2n(z))/(n+μ). The interesting point is that he obtained new explicit expressions for the sum of the series. In this note we point out that some results of Newberger are not correct, especially the results obtained by the principle of analytic continuation. Our remarks include a correction for his important result for the series ∑Jn(z)Jn−m(z)/(n+μ).