Geodesic
On Orthogonality Relations for Dual Discrete $q$-Ultraspherical Polynomials
Symmetry, integrability and geometry: methods and applications, Tome 2 (2006) Cet article a éte moissonné depuis la source Math-Net.Ru

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The dual discrete $q$-ultraspherical polynomials $D_n^{(s)}(\mu(x;s)|q)$ correspond to indeterminate moment problem and, therefore, have one-parameter family of extremal orthogonality relations. It is shown that special cases of dual discrete $q$-ultraspherical polynomials $D_n^{(s)}(\mu(x;s)|q)$, when $s=q^{-1}$ and $s=q$, are directly connected with $q^{-1}$-Hermite polynomials. These connections are given in an explicit form. Using these relations, all extremal orthogonality relations for these special cases of polynomials $D_n^{(s)}(\mu(x;s)|q)$ are found.
Keywords: $q$-orthogonal polynomials; dual discrete $q$-ultraspherical polynomials; $q^{-1}$-Hermite polynomials; orthogonality relation. 
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     title = {On {Orthogonality} {Relations} for {Dual} {Discrete} $q${-Ultraspherical} {Polynomials}},
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Valentyna A. Groza; Ivan I. Kachuryk. On Orthogonality Relations for Dual Discrete $q$-Ultraspherical Polynomials. Symmetry, integrability and geometry: methods and applications, Tome 2 (2006). http://geodesic.mathdoc.fr/item/SIGMA_2006_2_a33/

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