Padé Approximants for Some q-Hypergeometric Functions
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We show that a large number of explicit formulas for Padé approximants for the ratios of basic hypergeometric functions result from an explicit expression given by Ismail and Rahman for the associated Askey-Wilson polynomials. By specializing this result and using a new transformation for basic hypergeometric series, we are able to recover a result due to Andrews, Goulden and Jackson. We also show how Padé approximants off the main diagonal can be constructed in this latter case.
KeywordsOrthogonal Polynomial Jacobi Polynomial Basic Hypergeometric Series Pade Approximants Formal Laurent Series
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