Synopsis
Excerpt from Infinite Determinants Associated With Hill's Equation<br/><br/>Hill's equation plays a role in many problems of electromagnetic theory. Its simplest form, Mathieu's equation arises in the problem of the diffraction by an elliptic cylinder. Generally Speaking, Hill's equation is the differ ential equation for a one-dimensional linear oscillator with a periodic potential. In most applications, the question of the existence of a periodic solution arises. The main purpose of this investigation is to examine the analytic character of the transcendental function whose zeros determine the periodic solutions....
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