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SUMMARY:Fast and stable rational approximation of generalized hypergeometr
 ic functions - Mikael Slevinsky (University of Manitoba)
DTSTART:20191210T160000Z
DTEND:20191210T163000Z
UID:TALK135529@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION: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 rad
 ii 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 Pad&eacute\; approximan
 ts. We will describe algorithms for their computation in linear time. This
  improvement\, over traditional algorithms with quadratic complexity\, als
 o increases their numerical stability and offers insight into the localiza
 tion of their poles.
LOCATION:Seminar Room 1\, Newton Institute
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