Displaying similar documents to “Growth of polynomials whose zeros are outside a circle”

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.

On maximum modulus for the derivative of a polynomial

K. Dewan, Sunil Hans (2009)

Annales UMCS, Mathematica

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If P(z) is a polynomial of degree n, having all its zeros in the disk [...] then it was shown by Govil [Proc. Amer. Math. Soc. 41, no. 2 (1973), 543-546] that [...] In this paper, we obtain generalization as well as improvement of above inequality for the polynomial of the type [...] Also we generalize a result due to Dewan and Mir [Southeast Asian Bull. Math. 31 (2007), 691-695] in this direction.

Inequalities concerning polar derivative of polynomials

Arty Ahuja, K. Dewan, Sunil Hans (2011)

Annales UMCS, Mathematica

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In this paper we obtain certain results for the polar derivative of a polynomial [...] , having all its zeros on [...] which generalizes the results due to Dewan and Mir, Dewan and Hans. We also obtain certain new inequalities concerning the maximum modulus of a polynomial with restricted 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...

Single polynomials that correspond to pairs of cyclotomic polynomials with interlacing zeros

James McKee, Chris Smyth (2013)

Open Mathematics

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We give a complete classification of all pairs of cyclotomic polynomials whose zeros interlace on the unit circle, making explicit a result essentially contained in work of Beukers and Heckman. We show that each such pair corresponds to a single polynomial from a certain special class of integer polynomials, the 2-reciprocal discbionic polynomials. We also show that each such pair also corresponds (in four different ways) to a single Pisot polynomial from a certain restricted class,...