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They do not apply to all functions and one of them does not really show up well for Horn’s functions, however they do provide a number of results for individual multiple

Levin, General order Pade-type rational approximants dened from double power series, J.. Levin, On accelerating the convergence of innite double series and

Stegun (Eds.), Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Dover, New York, 1965..

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Most of the current theory and all implementations of Zeilberger’s algorithm remain restricted to the case of identities for terminating hypergeometric series, while many of the