On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials

Details On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials

2006-03-16

arxiv.org/abs/math/0603408v1

SIGMA 2 (2006), 034, 8 pages

Mathematics

Classical Analysis and ODEs

Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Scientific paper

10.3842/SIGMA.2006.034

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.

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