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SIGMA 2 (2006), 034, 8 pages math.CA/0603408
https://doi.org/10.3842/SIGMA.2006.034
On Orthogonality Relations for Dual Discrete q-Ultraspherical Polynomials
Valentyna A. Groza a and Ivan I. Kachuryk b
a) National Aviation University, 1 Komarov Ave., Kyiv, 03058 Ukraine
b) Khmel'nyts'kyi National University, Khmel'nyts'kyi, Ukraine
Received February 14, 2006, in final form February 28, 2006; Published online March 16, 2006
Abstract
The dual discrete q-ultraspherical polynomials
Dn(s)(μ(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 Dn(s)(μ(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 Dn(s)(μ(x;s)|q) are found.
Key words:
q-orthogonal polynomials; dual discrete q-ultraspherical polynomials; q-1-Hermite polynomials; orthogonality relation.
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