Classical biorthogonal rational functions

  • Mizan Rahman
  • S. K. Suslov
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1550)


A general set of biorthogonal rational functions, considered previously by Rahman and Wilson, is shown to satisfy a second-order linear difference equation of a nonuniform lattice. In the spirit of Hahn’s approach for orthogonal polynomials, raising and lowering operators as well as a Rodriguez-type formula are obtained for these functions which contain the classical orthogonal polynomials as limiting cases. Their biorthogonality in the discrete case is established by means of a Sturm-Liouville type argument. An outline of Wilson’s technique for representing them as Gram determinants is also given.


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Copyright information

© The Euler International Mathematical Institute 1993

Authors and Affiliations

  • Mizan Rahman
    • 1
  • S. K. Suslov
    • 2
  1. 1.Dept. of Mathematics and StatisticsCarleton UniversityOttawaCanada
  2. 2.Kurchatov Institute of Atomic EnergyMoscowRussia

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