Displaying similar documents to “On the complex zeros of some families of orthogonal polynomials.”

Differential equations associated with generalized Bell polynomials and their zeros

Seoung Cheon Ryoo (2016)

Open Mathematics

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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.

Extention of Apolarity and Grace Theorem

Sendov, Blagovest, Sendov, Hristo (2013)

Mathematica Balkanica New Series

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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...

On zeros of regular orthogonal polynomials on the unit circle

P. García Lázaro, F. Marcellán (1993)

Annales Polonici Mathematici

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A new approach to the study of zeros of orthogonal polynomials with respect to an Hermitian and regular linear functional is presented. Some results concerning zeros of kernels are given.

Growth of polynomials whose zeros are outside a circle

K. Dewan, Sunil Hans (2008)

Annales UMCS, Mathematica

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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.