Applications of q-Taylor theorems

  • Authors:

  • Mourad E. H. Ismail;Dennis Stanton

  • Affiliations:

  • Department of Mathematics, University of South Florida, Tampa, FL;School of Mathematics, University of Minnesota, Minneapolis, MN

  • Venue:
  • Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
  • Year:
  • 2003

Quantified Score

Hi-index 0.00

Visualization

Abstract

We establish two new q-analogues of a Taylor series expansion for polynomials using special Askey-Wilson polynomial bases. Combining these expansions with an earlier expansion theorem we derive inverse relations and evaluate certain linearization coefficients. Byproducts include new summation theorems, new results on a q-exponential function, and quadratic transformations for q-series.