Abstract
In this paper we shall be concerned with the derivation of simple expressions for the sums of some infinite series involving the zeros of Bessel functions of the first kind. For instance, if we denote by γv, n (n = l, 2, 3,…) the positive zeros of Jv(z), then, in certain physical applications, we are interested in finding the values of the sumsandwhere m is a positive integer. In § 4 of this paper we shall derive a simple recurrence relation for S2m,v which enables the value of any sum to be calculated as a rational function of the order vof the Bessel function. Similar results are given in § 5 for the sum T2m,v.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Reference5 articles.
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2. The expression of Bessel functions of positive order as products, and their inverse powers as sums of rational fractions;Forsyth;Messenger of Math.,1920
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