A Note on Summation of Kapteyn Series in Astrophysical Problems

Details A Note on Summation of Kapteyn Series in Astrophysical Problems A Note on Summation of Kapteyn Series in Astrophysical Problems

Aug 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007apj...665.1288l&link_type=abstract

The Astrophysical Journal, Volume 665, Issue 2, pp. 1288-1291.

Astronomy and Astrophysics

Astronomy

5

Stars: Pulsars: General

Scientific paper

In problems concerning the rate of radiation and radiation force of magnetized pulsars, there arise sequences of infinite series of Bessel functions that are generalized Kapteyn series of the second kind. To date, closed-form solutions for such series have proven elusive. The general procedure for effecting closed form solutions is given here, and the infinite series is summed so that there is now no need to resort to approximations that are not easy to justify. In other astrophysical problems, where similar series can arise, the method presented here can be used to simplify otherwise cumbersome results and to present general analytical formulae.

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