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Padé Approximants for Some q-Hypergeometric Functions

  • Mourad E. H. Ismail
  • Ron Perline
  • Jet Wimp
Conference paper
  • 267 Downloads
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 19)

Abstract

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.

Keywords

Orthogonal Polynomial Jacobi Polynomial Basic Hypergeometric Series Pade Approximants Formal Laurent Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Mourad E. H. Ismail
    • 1
  • Ron Perline
    • 2
  • Jet Wimp
    • 2
  1. 1.Department of MathematicsUniversity of South FloridaTampaUSA
  2. 2.Department of Mathematics and Computer ScienceDrexel UniversityPhiladelphiaUSA

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