Abstract
Kapteyn series of the second kind appear in models of even- and odd-order sideband spectra in the optical regime of a quantum system modulated by a high-frequency (e.g., terahertz) electromagnetic field (Citrin D S 1999 Phys. Rev. B 60 5659) and in certain time-periodic transport problems in superlattices (Ignatov A A and Romanov Y A 1976 Phys. Status Solidi b 73 327; Feise M W and Citrin D S 1999 Appl. Phys. Lett. 75 3536). This paper shows that both the even- and the odd-order Kapteyn series that appear can be summed in closed form, thereby allowing more transparent insight into the structural dependence of the sideband spectra and also providing an analytic control for the accuracy of numerical procedures designed to evaluate the series. The general method of analysis may also be of interest for other Kapteyn series.
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