q-Taylor theorems, polynomial expansions, and interpolation of entire functions

Mourad E.H. Ismail, Dennis Stanton

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


We establish q-analogues of Taylor series expansions in special polynomial bases for functions analytic in bounded domains and for entire functions whose maximum modulus M(r;f) satisfies 1n M(r;f) ≤A 1n2 r. This solves the problem of constructing such entire functions from their values at [aqn + q-n /a]/2, for 0<q<1. Our technique is constructive and gives an explicit representation of the sought entire function. Applications to q-series identities are given.

Original languageEnglish (US)
Pages (from-to)125-146
Number of pages22
JournalJournal of Approximation Theory
Issue number1
StatePublished - Jul 1 2003


  • Askey-Wilson operators
  • Carlson's theorem
  • Integral representations
  • Polynomial bases
  • q-Taylor series
  • q-exponential function


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