Stanisław Lewanowicz

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Let fP n (x)g 1 n=0 and fQ m (x)g 1 m=0 be two families of orthogonal polynomials. The linearization problem involves only one family via the relation: P i (x) P j (x) = i+j X k=ji?jj L ijk P k (x) and the connection problem mixes both families: P n (x) = n X m=0 C m (n) Q m (x): In many cases, it is possible to build a recurrence relation involving only m(More)
Extending the results of [1] (see also [2]), we introduce the polynomials of the vector variable x ∈ R d , depending on two parameters q and ω, which generalize the classical multivariate Bernstein polynomials. For ω = 0, we obtain an extension of univariate q-Bernstein polynomials, recently introduced by Phillips [3]. Among the properties of the new(More)
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