Related papers: Polynomials Whose Coefficients Coincide with Their…

In this paper, we will discuss the notion of almost orthogonality in a functional sequence.Especially, we will define a few sequences of almost orthogonal polynomials which can be used successfully for modeling of electronic systems which…

Interpolation polynomials were introduced by Knop--Sahi in type $A$, and Okounkov in type $BC$. They are inhomogeneous polynomials whose top terms are Jack and Macdonald polynomials. Thus the expansion coefficients for the product of two…

The purpose of this note is to establish, from the hypergeometric-type difference equation introduced by Nikiforov and Uvarov, new tractable sufficient conditions for the monotonicity with respect to a real parameter of zeros of classical…

In this paper, we obtain several new classes of irreducible polynomials having integer coefficients whose zeros lie inside an open disk around the origin or outside a closed annular region in the complex plane. Such irreducible polynomials…

A time-dependent monic polynomial in the z variable with N distinct roots such that exactly one root has multiplicity m>=2 is considered. For k=1,2, the k-th derivatives of the N roots are expressed in terms of the derivatives of order j<=…

Let $E = \cup_{j = 1}^l [a_{2j-1},a_{2j}],$ $a_1 < a_2 < ... < a_{2l},$ $l \geq 2$ and set ${\boldmath$\omega$}(\infty) =(\omega_1(\infty),...,\omega_{l-1}(\infty))$, where $\omega_j(\infty)$ is the harmonic measure of $[a_{2 j - 1}, a_{2…

We study the asymptotic properties of monic orthogonal polynomials (OPs) with respect to some Freud weights when the degree of the polynomial tends to infinity, including the asymptotics of the recurrence coefficients, the nontrivial…

We introduce a notion of asymptotically orthonormal polynomials for a Borel measure $\mu$ with compact nonpolar support in $\mathbb{C}$. Such sequences of polynomials have similar convergence properties of the sequences of Julia sets and…

Using a variety of matrix techniques, the problem of locating the left eigenvalues of the quaternion companion matrices are investigated in this paper. In a recent paper, Dar et al. [6], proved that the zeros of a quaternionic polynomial…

We study sets of univariate hyperbolic polynomials that share the same first few coefficients and show that they have a natural combinatorial description akin to that of polytopes. We define a stratification of such sets in terms of root…

In this paper, we explore (slightly generalized) $f$-Eulerian polynomials introduced by Stanley and frequently appearing in combinatorics. Notable special cases include the classical Eulerian polynomials, the generating polynomials of order…

In this paper, we introduce polynomials (in $t$) of signed relative derangements that track the number of signed elements. The polynomials are clearly seen to be in a sense symmetric. Note that relative derangements are those without any…

A new method of algebraic nature is proposed for the study of the asymptotic properties of special polynomials. The technique we foresee is based on the use of umbral operators, allowing a unified treatment of a large body of polynomial…

The affine Hecke algebra of type $A$ has two parameters $\left( q,t\right) $ and acts on polynomials in $N$ variables. There are two important pairwise commuting sets of elements in the algebra: the Cherednik operators and the Jucys-Murphy…

In this article we study the limiting empirical measure of zeros of higher derivatives for sequences of random polynomials. We show that these measures agree with the limiting empirical measure of zeros of corresponding random polynomials.…

In this paper, a fourth-order partial divided-difference equation on quadratic lattices with polynomial coefficients satisfied by bivariate Racah polynomials is presented. From this equation we obtain explicitly the matrix coefficients…

In this article, we propose a few sufficient conditions on polynomials having integer coefficients all of whose zeros lie outside a closed disc centered at the origin in the complex plane and deduce the irreducibility over the ring of…

We show that smooth curves of monic complex polynomials $P_a (Z)=Z^n+\sum_{j=1}^n a_j Z^{n-j}$, $a_j : I \to \mathbb C$ with $I \subset \mathbb R$ a compact interval, have absolutely continuous roots in a uniform way. More precisely, there…

An approach is proposed for bounding the number of zeros that solutions of linear differential systems with polynomial coefficients may have. A bound is obtained in a special case which improves upon currently existing.

A new numerical method is introduced for calculation of quasi-polynomial zeros with constant single delay. The trajectories of zeros are obtained depending on time-delay from zero to final time-delay value. The method determines all the…