Displaying similar documents to “Differential equations associated with generalized Bell polynomials and their zeros”

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...

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.

Remarks on some recent results about polynomials with restricted zeros

M. A. Qazi (2013)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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We point out certain flaws in two papers published in Ann. Univ. Mariae Curie-Skłodowska Sect. A, one in 2009 and the other in 2011. We discuss in detail the validity of the results in the two papers in question.