On convergence of basic hypergeometric series

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  • Representation Theory and Differential Equations : Proceedings of JMM Workshop on Representation Theory and Differential Equations,November 26-27,2016 Josai University

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We examine the convergence of q-hypergeometric series when |q| = 1. We give a condition so that the radius of the convergence is positive and get the radius. We also show that the numbers q with the positive radius of the convergence are densely distributed in the unit circle of the complex plane of q and so are those with the radius 0. First we give an elementary proof of this result and then an extended result.

identifier:JOS-13447777-1013

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