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

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