Geodesic
Application of Krein’s series to calculation of sums containing zeros of the Bessel functions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4, pp. 575-581 
E. V. Sumin; V. B. Sherstyukov. Application of Krein’s series to calculation of sums containing zeros of the Bessel functions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 4, pp. 575-581. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_4_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The Bessel functions of the first kind, $J_{\mathrm{v}}(z)$, with $\mathrm{v}>-1$ are considered. On the basis of the general theorem on the representation of the reciprocal of an entire function in the form of Krein’s series, an expansion of the function $1/J_{\mathrm{v}}(z)$ in simple fractions is obtained. This result is used to calculate the sums of series of a certain structure that contain powers of positive zeros of Bessel functions.

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