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Fast and stable rational approximation of generalized hypergeometric functions

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CATW03 - Computational complex analysis

Generalized hypergeometric functions are a central tool in the theory of special functions and complex analysis. Rational approximation permits analytic continuation of formal power series well beyond their radii of convergence. In this talk, we will use sequence transformations to convert successive partial sums of generalized hypergeometric series into rational approximants, which are in certain cases Padé approximants. We will describe algorithms for their computation in linear time. This improvement, over traditional algorithms with quadratic complexity, also increases their numerical stability and offers insight into the localization of their poles.

This talk is part of the Isaac Newton Institute Seminar Series series.

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