ABSTRACT
Vibrations of distributed systems in domains with elliptic (in particular, circular) boundary is an object of numerous investigations in the theory of elasticity (plates and membranes), hydrodynamics, acoustics, electrodynamics (resonators), etc. In spite of the fact that such problems are formulated very simply and admit partial separation of spatial variables in elliptic coordinates, their numerical solution for large eccentricity values is difficult. For this purpose, new classes of special functions have been introduced. Great achievements in this field should be credited to Mathieu, Rayleigh, Ince, Strutt, McLachlan, Sretensky, and others.
