Arithmetized trigonometrical expansions of doubly periodic functions of the third kind

Abstract

In a series of papers, Appell (1) discusses the problem of exhibiting a function, G(z), meromorphic and uniform, and satisfying the equations of definition G(z + π) = G(z) G(z + π τ) = e^-2miz G(z) m an integer >< 0 as a sum of simple elements, each having a single singularity in a period parallogram, and an integral function of z.

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