On certain Fourier series expansions of doubly periodic functions of the third kind
It is a well-known fact that the Fourier series expansions of the doubly periodic functions of the first (i.e., elliptic), second and third kinds (in the sense of Hermite) yield, when subjected to appropriate methods, important results in the theory of numbers. The purpose of this paper is to indicate the derivation of such expansions for certain doubly periodic functions of the third kind of a type having a larger number of zeros than poles .
Copyright ©1929 by the National Academy of Sciences. Presented to the American Mathematical Society, Oct. 27, 1928. Communicated June 26, 1929. The complete details of these expansions may be found in a dissertation by the writer which is deposited in the library of the California Institute of Technology.
Published - BASpnas29.pdf