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Mathematical Essays in honor of Gian-Carlo Rota pp 377–396Cite as

More Orthogonal Polynomials as Moments

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Part of the book series: Progress in Mathematics ((PM,volume 161))

Abstract

Classical orthogonal polynomials as moments for other classical orthogonal polynomials are obtained via linear functionals. The combinatorics of the Al-Salam-Chihara polynomials are given, and three classification theorems for generalized moments as orthogonal polynomials are proven. Some combinatorial explanations and open problems are discussed.

This work was supported by NSF grant DMS-9625459 and a research fellowship from the Leverhulme Foundation.

This work was supported by NSF grant DMS-9400510.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of South Florida, 33620, Tampa, FL, USA

    Mourad E. H. Ismail

  2. School of Mathematics, University of Minnesota, 55455, Minneapolis, MN, USA

    Dennis Stanton

Authors
  1. Mourad E. H. Ismail
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  2. Dennis Stanton
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Michigan State University, 48824, East Lansing, MI, USA

    Bruce E. Sagan

  2. Department of Mathematics, MIT, 02139, Cambridge, MA, USA

    Richard P. Stanley

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© 1998 Birkhäuser

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Ismail, M.E.H., Stanton, D. (1998). More Orthogonal Polynomials as Moments. In: Sagan, B.E., Stanley, R.P. (eds) Mathematical Essays in honor of Gian-Carlo Rota. Progress in Mathematics, vol 161. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-4108-9_20

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  • DOI: https://doi.org/10.1007/978-1-4612-4108-9_20

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-1-4612-8656-1

  • Online ISBN: 978-1-4612-4108-9

  • eBook Packages: Springer Book Archive

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