• 통합자연과학논문집
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• 제4권3호
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• pp.227-228
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• 2011

Bae and Kim displayed a sequence of 4th degree self-reciprocal polynomials whose maximal zeros are related in a very nice and far from obvious way. The auxiliary polynomials in their results that parametrize their coefficients are of significant independent interest. In this note we show that such auxiliary polynomials are related to Chebyshev polynomials.

• Korean Journal of Mathematics
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• 제31권2호
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• pp.153-160
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• 2023

In this paper, we study the growth of polynomials P(z) of degree n defined by $P(z)=z^s(a_0+\sum\limits_{j=t}^{n-s}a_jz^j)$, t ≥ 1, 0 ≤ s ≤ n-1 which do not vanish in the disk |z| ≤ k, k ≥ 1 except for the s-fold zeros at origin. Our result generalises and refines many results known in the literature.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.315-322
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• 2014

In this paper, we observe the behavior of complex roots of the tangent polynomials $T_n(x)$, using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the tangent polynomials $T_n(x)$. Finally, we give a table for the solutions of the tangent polynomials $T_n(x)$.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.733-747
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• 2021

Recently, Kim-Kim introduced Lah-Bell polynomials and numbers, and investigated some properties and identities of these polynomials and numbers. Kim studied Lah-Bell polynomials and numbers of degenerate version. In this paper, we study degenerate Lah-Bell polynomials arising from differential equations. Moreover, we investigate the phenomenon of scattering of the zeros of these polynomials.

• Korean Journal of Mathematics
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• 제30권2호
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• pp.413-423
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• 2022

In this paper, we prove some results concerning the zeros of Bi-complex polynomials. These results as special cases include Grace's theorem and related results.

• Journal of applied mathematics & informatics
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• 제36권5_6호
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• pp.475-489
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• 2018

In this paper, by using the polylogarithm function, we introduce a generalized poly-Bernoulli numbers and polynomials with variable a. We find several combinatorial identities and properties of the polynomials. We give some properties that is connected with the Stirling numbers of second kind. Symmetric properties can be proved by new configured special functions. We display the zeros of the generalized poly-Bernoulli polynomials with variable a and investigate their structure.

• Journal of applied mathematics & informatics
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• 제35권5_6호
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• pp.495-504
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• 2017

In this paper we construct the Carlitz's type q-tangent numbers $T_{n,q}$ and polynomials $T_{n,q}(x)$. From these numbers and polynomials, we establish some interesting identities and relations.

• 대한수학회논문집
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• 제34권2호
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• pp.429-437
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• 2019

Dilcher and Stolarsky [1] recently studied a sequence resembling the Chebyshev polynomials of the first kind. In this paper, we follow their some research directions to the Chebyshev polynomials of the second kind. More specifically, we consider a sequence resembling the Chebyshev polynomials of the second kind in two different ways, and investigate its properties including relations between this sequence and the sequence studied in [1], zero distribution and the irreducibility.

• 대한수학회보
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• 제46권6호
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• pp.1153-1158
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• 2009

Given two integral self-reciprocal polynomials having the same modulus at a point $z_0$ on the unit circle, we show that the minimal polynomial of $z_0$ is also self-reciprocal and it divides an explicit integral self-reciprocal polynomial. Moreover, for any two integral self-reciprocal polynomials, we give a sufficient condition for the existence of a point $z_0$ on the unit circle such that the two polynomials have the same modulus at $z_0$.

• Kyungpook Mathematical Journal
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• 제53권4호
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• pp.541-552
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• 2013

This research is a continuation of a recent paper due to the first author in [9]. Different from previous results, we investigate the value distribution of difference polynomials of moromorphic functions in this paper. In particular, we are interested in the existence of zeros of $f(z)^n({\lambda}f(z+c)^m+{\mu}f(z)^m)-a$, where f is a moromorphic function, n, m are two non-negative integers, and ${\lambda}$, ${\mu}$ are non-zero complex numbers. However, the proof here is obviously different to the one in [9]. We also study difference polynomials of entire functions sharing a common value, which improves the result in [10, 13].