On certain Fourier series expansions of doubly periodic functions of the third kind

Abstract

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 [2].

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