Curious q-Series as Counterexamples in Padé Approximation
Basic hypergeometric, or q-series, are usually investigated when |q| < 1. Less common is the case |q| > 1, and the case where q is on the unit circle is extremely rare. It is the latter curious, exotic, choice of q that has yielded a number of interesting examples and counterexamples in Padé approximation, including a counterexample to the Baker-Gammel-Wills Conjecture. We survey some of these, and also pose a number of problems involving q-series for q on the unit circle.
KeywordsCompact Subset Unit Circle Unit Ball Continue Fraction Formal Power Series
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