Results 21 to 30 of about 1,536 (263)

Schur-Type Inequalities for Complex Polynomials with no Zeros in the Unit Disk

Journal of Inequalities and Applications, 2007
Starting out from a question posed by T. Erdélyi and J. Szabados, we consider Schur-type inequalities for the classes of complex algebraic polynomials having no zeros within the unit disk D.
Szilárd Gy. Révész
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Complementary Romanovski-Routh polynomials and their zeros

Trends in Computational and Applied Mathematics
The efficacy of numerical methods like integral estimates via Gaussian quadrature formulas depends on the localization of the zeros of the associated family of orthogonal polynomials.
L. L. Silva Ribeiro, A. Sri Ranga, Yen Chi Lun   +2 more
doaj   +1 more source

Bounding the Zeros of Polynomials Using the Frobenius Companion Matrix Partitioned by the Cartesian Decomposition

Algorithms, 2022
In this work, some new inequalities for the numerical radius of block n-by-n matrices are presented. As an application, the bounding of zeros of polynomials using the Frobenius companion matrix partitioned by the Cartesian decomposition method is proved.
Mohammad W. Alomari, Christophe Chesneau
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On the Zeros of Polynomials

Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics, 1977
1. Govil and Rahman [1, Theorem 1] have proved the fol- lowing theorem.n Theorem A. Let p (z) = £ aj^ k“0 z’^ ( 0) be a polynomiai ofdegree n with complex coefficients such that for some a>«-1 I a^ •11-2 a' I »ol-Then p (z) has ali its zeros in |z Kj, where Kj is the greatest positive root of the trinomial equation K"+ı - 2K" + 1 =
openaire   +4 more sources

Analytic Continuation of Euler Polynomials and the Euler Zeta Function

Discrete Dynamics in Nature and Society, 2014
We study that the Euler numbers En and Euler polynomials Enz are analytically continued to Es and E(s,w). We investigate the new concept of dynamics of the zeros of analytica continued polynomials.
C. S. Ryoo
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On zeros of polynomial

Ufimskii Matematicheskii Zhurnal, 2019
Summary: For a given polynomial \[P\left( z\right) =z^n+a_{n-1}z^{n-1}+a_{n-2}z^{n-2}+\cdots +a_1z+a_0\] with real or complex coefficients, the Cauchy bound \[\left\vert z\right\vert
openaire   +1 more source

A Note on the (ℎ,𝑞)-Extension of Bernoulli Numbers and Bernoulli Polynomials

Discrete Dynamics in Nature and Society, 2010
We observe the behavior of roots of the (ℎ,𝑞)-extension of Bernoulli polynomials 𝐵(ℎ)𝑛,𝑞(𝑥). By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the q-extension of Bernoulli polynomials 𝐵(ℎ)𝑛,𝑞(𝑥). The
C. S. Ryoo, T. Kim
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On the Zeroes of a Polynomial

Journal of Approximation Theory, 1995
Improving on a result of \textit{J. L. Walsh} [Ann. Math., II. Ser. 25, 285-296 (1924; JFM 50.0045.03)], the author offers the inequality \[ |z+ (a_{n- 1}/2)|\leq |a_{n- 1} |/2+ \Biggl[\sum^n_{j= 2} |a_{n- j}|(\max_{2\leq k\leq n} |a_{n- k}|^{(2- j)/k})^{1/2}\Biggr] \] for zeroes of \(\sum^{n- 1}_{j= 0} a_j z^j+ z^n\) \((n\geq 2)\).
openaire   +1 more source

Some Identities for Euler and Bernoulli Polynomials and Their Zeros

Axioms, 2018
In this paper, we study some special polynomials which are related to Euler and Bernoulli polynomials. In addition, we give some identities for these polynomials. Finally, we investigate the zeros of these polynomials by using the computer.
Taekyun Kim, Cheon Seoung Ryoo
doaj   +1 more source

Square Roots of Real 3 × 3 Matrices vs. Quartic Polynomials with Real Zeros

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017
There is an interesting analogy between the description of the real square roots of 3×3 matrices and the zeros of the (depressed) real quartic polynomials.
Anghel Nicolae
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