On the natural \(q^2\)-analogue of the generalized Gegenbauer form. (English) Zbl 1314.33008

Ben Salah, I.; Khériji, L.

Transylv. J. Math. Mech. 6, No. 1, 59-68 (2014).

Summary: The aim of this paper is to highlight a \(q^2\)-analogue of the generalized Gegenbauer polynomials orthogonal with respect to the form \(\mathcal{G}(\alpha,\beta,q^2)\). Integral representation and discrete measure of \(\mathcal{G}(\alpha,\beta,q^2)\) are given for some values of parameters.

MSC:

33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
42C05	Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis

Keywords:

\(q\)-difference operator; \(H_q\)-semiclassical form; \(q\)-distributional equation; moments; discrete measure; integral representation