A 𝑞-beta integral on the unit circle and some biorthogonal rational functions
Copyright policy )A 𝑞-beta integral on the unit circle and some biorthogonal rational functions
In this paper we first consider a pair of polynomial sets which are biorthogonal on the unit circle with respect to a complex weight function. We then show how the biorthogonality of this pair of polynomial sets implies aq-beta integral which in turn leads to a pair of biorthogonal rational functions. Finally we show that the asymptotics for these pairs of rational functions exhibit qualitative properties reminiscent of the Szegö theory for orthogonal polynomials.
biorthogonal sets of polynomials, asymptotics of biorthogonal rational functions, \(q\)-beta integral, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), biorthogonal sets of functions, \(q\)-gamma functions, \(q\)-beta functions and integrals, Completeness of sets of functions in one variable harmonic analysis
biorthogonal sets of polynomials, asymptotics of biorthogonal rational functions, \(q\)-beta integral, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), biorthogonal sets of functions, \(q\)-gamma functions, \(q\)-beta functions and integrals, Completeness of sets of functions in one variable harmonic analysis
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