# Search results for: Juan J. Moreno-Balcázar

Indagationes Mathematicae > 2004 > 15 > 2 > 151-165

_{n}

^{(}

^{α}

^{,}

^{M}

^{,}

^{N}

^{)}(x) orthogonal with respect to the Sobolev inner product (p,q) = 1 (α+1)∫0~p(x)q(x)x

^{α}e

^{-}

^{x}dx + Mp(O)q(O) + Np'(O)q'(O), N, M >= O, α > -I , firstly introduced by Koekoek and Meijer in 1993 and extensively studied in the last years. We present some new asymptotic properties...

Journal of Approximation Theory > 2003 > 125 > 1 > 26-41

_{S}=∫fgdμ+λ∫f'g'dμand we characterize the measures μ for which there exists an algebraic relation between the polynomials, {P

_{n}}, orthogonal with respect to the measure μ and the polynomials, {Q

_{n}}, orthogonal with respect to (*), such that the number of involved terms does not depend on the degree of the polynomials...

Journal of Approximation Theory > 2003 > 122 > 1 > 79-96

_{n}be polynomials orthogonal with respect to the inner product(f,g)

_{S}=∫0~fgdμ

_{0}+λ∫0~f'g'dμ

_{1},where dμ

_{0}=x

^{α}e

^{-}

^{x}dx,dμ

_{1}=x

^{α}

^{+}

^{1}e

^{-}

^{x}x-ξdx+Mδ

_{ξ}with α>-1,ξ=<0,M>=0, and λ>0. A strong asymptotic on (0,~), a Mehler-Heine type formula, a Plancherel-Rotach type exterior asymptotic...

Journal of Computational and Applied Mathematics > 2003 > 150 > 1 > 25-35

_{S}=∫f(x)g(x)dμ

_{0}(x)+λ∫f'(x)g'(x)dμ

_{1}(x),λ>0,with (μ

_{0},μ

_{1}) being a symmetrically coherent pair of measures with unbounded support. Denote by Q

_{n}the orthogonal polynomials with respect to (1) and they are so-called Hermite-Sobolev orthogonal polynomials. We give a Mehler-Heine-type formula for...

Journal of Computational and Applied Mathematics > 2001 > 133 > 1-2 > 141-150

_{n}be the polynomials orthogonal with respect to the Sobolev inner product(f,g)

_{S}=∫fgdμ

_{0}+∫f'g'dμ

_{1},being (μ

_{0},μ

_{1}) a coherent pair where one of the measures is the Hermite measure. The outer relative asymptotics for Q

_{n}with respect to Hermite polynomials are found. On the other hand, we consider the Sobolev scaled polynomials and...

Journal of Computational and Applied Mathematics > 1997 > 81 > 2 > 217-227

_{n}(x), orthogonal with respect to the inner product (f,g)s = ∫ f(x)g(x)dμ

_{1}(x) + λ ∫ f (x)g (x)dμ

_{2}(x), λ>0, with x outside of the support of the measure μ

_{2}. We assume that μ

_{1}and μ

_{2}are symmetric and compactly supported measures on R satisfying a coherence condition...

Journal of Computational and Applied Mathematics > 1997 > 81 > 2 > 211-216

^{1}

_{-}

_{1}f(x)g(x(1 - x

^{2})

^{α}

^{-}

^{1}

^{2}dx with α > - 12 and λ > 0. The asymptotics of the zeros and norms of these polynomials are also established.