XXII.—Tables of the Elliptic-cylinder Functions

Abstract

Although the physical problem which originally led to the Mathieu equationis now well over sixty years old, and although other problems studied in more recent years, such as the scattering of electric waves by an elliptic cylinder, depend essentially on the same equation, no thorough investigation of detail has hitherto been possible owing to the lack of tables of the functions defined by the equation. In fact, until 1924 all attempts to reduce the functions to a form suitable for calculation had failed. In that year a successful method of attack was discovered by the present writer, who then undertook the computation of the tables which are here published.