polynomial

About Asymptotic Polynomials, Orthogonal on Any Grids

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.

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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 pˆ^α,β_n(x), orthogonal with weight (1−x_j)^α(1+x_j)^β∆t_jon 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.

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On the Choice of Approximation for Number of Elements in the Sequence of Values for Simple Polynomial of Argument pq with Constraints on p and q

Authors: Vakhitova E. V., Vakhitova S. R.

In this paper the theorem is obtained on one choice of the approximation for the element number in finite sequence of special kind.

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