Displaying similar documents to “On zeros of regular orthogonal polynomials on the unit circle”

Differential equations associated with generalized Bell polynomials and their zeros

Seoung Cheon Ryoo (2016)

Open Mathematics

Similarity:

In this paper, we study differential equations arising from the generating functions of the generalized Bell polynomials.We give explicit identities for the generalized Bell polynomials. Finally, we investigate the zeros of the generalized Bell polynomials by using numerical simulations.

On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem

Abdullah Mir (2023)

Czechoslovak Mathematical Journal

Similarity:

We present some results on the location of zeros of regular polynomials of a quaternionic variable. We derive new bounds of Eneström-Kakeya type for the zeros of these polynomials by virtue of a maximum modulus theorem and the structure of the zero sets of a regular product established in the newly developed theory of regular functions and polynomials of a quaternionic variable. Our results extend some classical results from complex to the quaternionic setting as well.

Extention of Apolarity and Grace Theorem

Sendov, Blagovest, Sendov, Hristo (2013)

Mathematica Balkanica New Series

Similarity:

MSC 2010: 30C10 The classical notion of apolarity is defined for two algebraic polynomials of equal degree. The main property of two apolar polynomials p and q is the classical Grace theorem: Every circular domain containing all zeros of p contains at least one zero of q and vice versa. In this paper, the definition of apolarity is extended to polynomials of different degree and an extension of the Grace theorem is proved. This leads to simplification of the conditions of...

Growth of polynomials whose zeros are outside a circle

K. Dewan, Sunil Hans (2008)

Annales UMCS, Mathematica

Similarity:

If p(z) be a polynomial of degree n, which does not vanish in |z| < k, k < 1, then it was conjectured by Aziz [Bull. Austral. Math. Soc. 35 (1987), 245-256] that [...] In this paper, we consider the case k < r < 1 and present a generalization as well as improvement of the above inequality.

A generalization of the Gauss-Lucas theorem

J. L. Díaz-Barrero, J. J. Egozcue (2008)

Czechoslovak Mathematical Journal

Similarity:

Given a set of points in the complex plane, an incomplete polynomial is defined as the one which has these points as zeros except one of them. The classical result known as Gauss-Lucas theorem on the location of zeros of polynomials and their derivatives is extended to convex linear combinations of incomplete polynomials. An integral representation of convex linear combinations of incomplete polynomials is also given.