Geodesic
On some infinite series involving the zeros of Bessel functions of the first kind
Glasgow mathematical journal, Tome 4 (1960) no. 3, pp. 144-156

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Sneddon, Ian N. On some infinite series involving the zeros of Bessel functions of the first kind. Glasgow mathematical journal, Tome 4 (1960) no. 3, pp. 144-156. doi: 10.1017/S2040618500034067
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