An estimate for coefficients of polynomials in norm. II.
Milovanović, G.V., Rančić, L.Z. (1995)
Publications de l'Institut Mathématique. Nouvelle Série
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Milovanović, G.V., Rančić, L.Z. (1995)
Publications de l'Institut Mathématique. Nouvelle Série
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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.
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.
Đurđe Cvijović, Jacek Klinowski (1998)
Matematički Vesnik
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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.
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...
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,...
Gutman, Ivan (1985)
Publications de l'Institut Mathématique. Nouvelle Série
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Simic, Slavko (2006)
Journal of Inequalities and Applications [electronic only]
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Alain Lascoux (1990)
Banach Center Publications
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P. E. Blanksby (1985)
Banach Center Publications
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Lubinsky, D.S. (1997)
Journal of Inequalities and Applications [electronic only]
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Inoue, Tetsuo (1996)
International Journal of Mathematics and Mathematical Sciences
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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.
Ruedemann, Richard W. (1994)
International Journal of Mathematics and Mathematical Sciences
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Radoš Bakić (2013)
Publications de l'Institut Mathématique
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