Classical biorthogonal rational functions
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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