相关论文: Chain sequences and Zeros of a perturbed $R_{II}$ …

This paper establishes the necessary and sufficient conditions for the reality of all the zeros in a polynomial sequence $\{P_i\}_{i=1}^{\infty}$ generated by a three-term recurrence relation $P_i(x)+ Q_1(x)P_{i-1}(x) +Q_2(x) P_{i-2}(x)=0$…

Systems of orthogonal polynomials whose recurrence coefficients tend to infinity are considered. A summability condition is imposed on the coefficients and the consequences for the measure of orthogonality are discussed. Also discussed are…

In this paper, we present a new method via the transfer matrix approach to obtain asymptotic formulae of orthogonal polynomials with asymptotically identical coefficients of bounded variation. We make use of the hyperbolicity of the…

A result of P\'olya states that every sequence of quadrature formulas $Q_n(f)$ with $n$ nodes and positive numbers converges to the integral $I(f)$ of a continuous function $f$ provided $Q_n(f)=I(f)$ for a space of algebraic polynomials of…

We give recurrence relations for any family of generalized Appell polynomials unifying so some known recurrences of many classical sequences of polynomials. Our main tool to get our goal is the Riordan group. We use the product of Riordan…

We show that the zeros of consecutive orthogonal polynomials $p_n$ and $p_{n-1}$ are linearly connected by a doubly stochastic matrix for which the entries are explicitly computed in terms of Christoffel numbers. We give similar results for…

We investigate the ratio asymptotic behavior of the sequence $(Q_{n})_{n=0}^{\infty}$ of multiple orthogonal polynomials associated with a Nikishin system of $p\geq 1$ measures that are compactly supported on the star-like set of $p+1$ rays…

Uvarov-type perturbations for mixed-type multiple orthogonal polynomials on the step line are investigated within a matrix-analytic framework. The transformations considered involve both rational and additive modifications of a rectangular…

A complete intersection of n polynomials in n indeterminates has only a finite number of zeros. In this paper we address the following question: how do the zeros change when the coefficients of the polynomials are perturbed? In the first…

For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…

We study statistics of resonances in a one-dimensional disordered chain coupled to an outer world simulated by a perfect lead. We consider a limiting case for weak disorder and derive some results which are new in these studies. The main…

We describe how the reversion of a series is related to convolutional recurrence relations for the series, and we place this relationship in the context of Riordan arrays. As an example of the approach, we give new recurrence relations for…

The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials…

For a linearly recurrent vector sequence P[n+1] = A(n) * P[n], consider the problem of calculating either the n-th term P[n] or L<=n arbitrary terms P[n_1],...,P[n_L], both for the case of constant coefficients A(n)=A and for a matrix A(n)…

Consider the number of permutations in the symmetric group on n letters that contain c copies of a given pattern. As c varies (with n held fixed) these numbers form a sequence whose properties we study for the monotone patterns and the…

We study linear transformations $T \colon \mathbb{R}[x] \to \mathbb{R}[x]$ of the form $T[x^n]=P_n(x)$ where $\{P_n(x)\}$ is a real orthogonal polynomial system. Such transformations that preserve or shrink the location of the complex zeros…

This paper derives sparse recurrence relations between orthogonal polynomials on a triangle and their partial derivatives, which are analogous to recurrence relations for Jacobi polynomials. We derive these recurrences in a systematic…

We study multiple orthogonal polynomials of type I and type II which have orthogonality conditions with respect to r measures. These polynomials are connected by their recurrence relation of order r+1. First we show a relation with the…

The relation between the spectral decomposition of a self-adjoint operator which is realizable as a higher order recurrence operator and matrix-valued orthogonal polynomials is investigated. A general construction of such operators from…

In Lett. Math. Phys. 114, 54 (2024) and 115, 70 (2025), the author introduces what is presented as a novel method for determining whether a sequence of orthogonal polynomials is "classical", based solely on its initial recurrence…