Abstract
also commonly known as the equation of the elliptic cylinder functions, is too well known to require any introduction. Its solutions govern problems of the greatest diversity in astronomy and theoretical physics, and have accordingly been the subjects of a vast number of investigations.t The differential equation as such depends upon two independent parameters, designated in the form written above by A and Q. In the present discussion these are to be taken real but are to be numerically unrestricted except that at least one is to be large. The variable will be permitted to range over the complex plane. Since the coefficient of the differential equation is an even simply periodic analytic function of z, it is known from Floquet's theory of such equations that the solutions are in general of the structure
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