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Polynomials, Orthogonal on Non-Uniform Grids

Authors: Nurmagomedov А. А.

Asymptotic properties of polynomials pˆn(t), orthogonal with weight ∆tj on any finite set of N points from segment [−1, 1] are investigated. Namely an asymptotic formula is proved in which asymptotic behaviour of these polynomials as n tends to infinity together with N is closely related to asymptotic behaviour of the Lasiandra polynomials. Furthermore are investigated the approximating properties of the sums by Fourier on these polynomials..

About Asymptotic Polynomials, Orthogonal on Any Grids

Authors: Magomedova Z. M.

Asymptotic properties of polynomials orthogonal ln(x), with weight e −xj ∆tj on any infinite set points from semi-axis [0, ∞) are investigated. Namely an asymptotic formula is proved in which asymptotic behaviour of these polynomials as n tends to infinity together with N is closely related to asymptotic behaviour of the polynomials by Lagerra.

Asymptotic Properties of Polynomials pˆα,βn (x), Orthogonal on Any Sets in the Сase of Integers α and β

Authors: Nurmagomedov А. А.

Asymptotic properties of polynomials pˆα,βn (x), orthogonal with weight (1−xj)α(1+xj)β∆tj on any finite set of N points from segment [−1,1] are investigated. Namely an asymptotic formula is proved in which asymptotic behaviour of these polynomials as n tends to infinity together with N is closely related to asymptotic behaviour of the Jacobi polynomials.