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Given {P n } n≥0 a sequence of monic orthogonal polynomials, we analyze their linear combinations with constant coefficients and fixed length, i.e.,

We consider a generalization of the classical Hermite polynomials by the addition of terms involving derivatives in the inner product. This type of generalization has been studied in the literature from the point of view of the algebraic properties. Thus, our aim is to study the asymptotics of this sequence of nonstandard orthogonal polynomials. In fact, we… (More)

Let { ℙ n } n ≥ 0 $\{\mathbb{P}_{n}\}_{n\ge 0}$ and { ℚ n } n ≥ 0 $\{\mathbb{Q}_{n}\}_{n\ge 0}$ be two monic polynomial systems in several variables satisfying the linear structure relation ℚ n = ℙ n + M n ℙ n − 1 , n ≤ 1 , $\mathbb{Q}_{n} = \mathbb{P}_{n} + M_{n} \mathbb{P}_{n-1}, \quad n\ge 1,$ where M n are constant matrices of proper size and ℚ 0 = ℙ 0… (More)

This paper deals with Mehler–Heine type asymptotic formulas for the so-called discrete Sobolev orthogonal polynomials whose continuous part is given by Laguerre and generalized Hermite measures. We use a new approach which allows to solve the problem when the discrete part contains an arbitrary (finite) number of mass points.

Let {Pn} n≥0 be a sequence of monic orthogonal polynomials with respect to a quasi–definite linear functional u and {Qn} n≥0 a sequence of polynomials defined by Qn(x) = Pn(x) + sn Pn−1(x) + tn Pn−2(x), n ≥ 1, with tn = 0 for n ≥ 2. We obtain a new characterization of the orthogonality of the sequence {Qn} n≥0 with respect to a linear functional v, in terms… (More)

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