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The Associated Classical Orthogonal Polynomials

  • Mizan Rahman
Part of the NATO Science Series book series (NAII, volume 30)

Abstract

The associated orthogonal polynomials p n (x;c) are defined by the 3-term recurrence relation with coefficients A n , B n , C n for p n (x) with c = 0, replaced by A n+c, B n+cand C n+c, c being the association parameter. Starting with examples where such polynomials occur in a natural way some of the well-known theories of how to determine their measures of orthogonality are discussed. The highest level of the family of classical orthogonal polynomials, namely, the associated Askey-Wilson polynomials which were studied at length by Ismail and Rahman in 1991 is reviewed with special reference to various connected results that exist in the literature.

Keywords

Classical orthogonal polynomials Associated orthogonal polynomials Associated Legendre, Laguerre, Hermite, Jacobi, q-ultraspherical, q-Jacobi and Askey-Wilson polynomials Continued fractions, Stieltjes transform, Perron-Stieltjes inversion formula Hypergeometric and basic hyper-geometric series 

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Mizan Rahman
    • 1
  1. 1.School of Mathematics & StatisticsCarleton UniversityOttawaCanada

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