
SIGMA 2 (2006), 034, 8 pages math.CA/0603408
http://dx.doi.org/10.3842/SIGMA.2006.034
On Orthogonality Relations for Dual Discrete qUltraspherical 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 qultraspherical polynomials
D_{n}^{(s)}(μ(x;s)q) correspond to indeterminate moment
problem and, therefore, have oneparameter family of extremal
orthogonality relations. It is shown that special cases of dual
discrete qultraspherical
polynomials D_{n}^{(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 D_{n}^{(s)}(μ(x;s)q) are found.
Key words:
qorthogonal polynomials; dual discrete qultraspherical polynomials; q^{1}Hermite polynomials; orthogonality relation.
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