Markov type polynomial inequality for some generalized Hermite weight

In this paper we study some weighted polynomial inequalities of Markov type in L²-norm. We use the properties of the system of generalized Hermite polynomials . The polynomials H^(α)_n (x) are orthogonal in ℝ = (−∞,∞) with respect to the weight function .

The classical Hermite polynomials H_n(x) present the special case for α = 0.