Approximate analytic continuation beyond the first Riemann sheet
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A brief review of the classical theory of multivalued functions of a complex variable is used to introduce the classification of monogenic analytic functions by their monodromic dimension. Riemann's monodromy theorem is used to set the stage for a class of Hermite-Padé multiform approximants. The approximation problem for functions meromorphic on a Riemann surface of m-sheets with a finite number of singular points is completely solved. A general uniqueness of convergence theorem and another convergence theorem are given.
KeywordsSingular Point Riemann Surface Entire Function Branch Point Meromorphic Function
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