Classical orthogonal polynomials as moments

Mourad E.H. Ismail, Dennis Stanton

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


We show that the Meixner, Pollaczek, Meixner-Pollaczek, the continuous q-ultraspherical polynomials and Al-Salam-Chihara polynomials, in certain normalization, are moments of probability measures. We use this fact to derive bilinear and multilinear generating functions for some of these polynomials. We also comment on the corresponding formulas for the Charlier, Hermite and Laguerre polynomials.

Original languageEnglish (US)
Pages (from-to)520-542
Number of pages23
JournalCanadian Journal of Mathematics
Issue number3
StatePublished - Jun 1997


  • Al-Salam-Chihara polynomials
  • Classical orthogonal polynomials
  • Continuous q-ultraspherical polynomials
  • Generating functions
  • Multilinear generating functions
  • Transformation formulas
  • Umbral calculus


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