• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1303-1308
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• 2018

In this paper, we consider both maximum modulus and minimum modulus on a circle of some polynomials. These give rise to interesting examples that are about moduli of Chebyshev polynomials and certain sums of polynomials on a circle. Moreover, we obtain some root locations of difference quotients of Chebyshev polynomials.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.7A
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• pp.1257-1263
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• 2001

In the paper, the p-ranks and characteristics polynomials of cyclic difference sets are derived by expanding the trace expression of their characteristic sequences. By using this method, it is shown that the 3-ranks and characteristic polynomials of Helleseth-Kumar-Martinsen (HKM) difference set and Lin difference set can be easily obtained.

• Journal of Applied and Pure Mathematics
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• v.5 no.5_6
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• pp.281-289
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• 2023

We investigate the value distribution of difference-differential polynomials of entire and meromorphic functions, which can be gazed as the Hayman's Conjecture. And also we study the uniqueness and existence for sharing common value of difference-differential polynomials.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.373-386
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• 2016

In this paper, we investigate analytic and algebraic properties, and derive some identities satisfied by difference quotients of Chebyshev polynomials of the first kind.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1429-1440
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• 2007

Let ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ be a multiple Kravchuk polynomial with respect to r discrete Kravchuk weights. We first find a lowering operator for multiple Kravchuk polynomials ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ in which the orthogonalizing weights are not involved. Combining the lowering operator and the raising operator by Rodrigues# formula, we find a (r+1)-th order difference equation which has the multiple Kravchuk polynomials ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ as solutions. Lastly we give an explicit difference equation for ${K^{(\vec{p};N)}_{\vec{n}}(x)}$ for the case of r=2.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.839-850
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• 2021

In this paper, we investigate the uniqueness problems of certain types of difference-differential polynomials of entire functions sharing a small function. The results of the paper improve and generalize the recent results due to Biswajit Saha [18].

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.549-565
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• 2024

In this paper, we investigate the uniqueness of linear difference differential polynomials sharing a small function. By using the concepts of weakly weighted and relaxed weighted sharing of transcendental entire functions with finite order, we obtained the corresponding results, which improve and extend some results of Chao Meng [14].

• Korean Journal of Mathematics
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• v.25 no.2
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• pp.181-199
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• 2017

In this paper we consider the orthogonal polynomials with weights ${\omega}_{\alpha}(x)=x^{\alpha}{\exp}(-x^3+tx)$ and $W_{\alpha}(x)={\mid}x{\mid}^{2{\alpha}+1}{\exp}(-x^6+tx^2)$. Using the compatibility conditions for the ladder operators for these orthogonal polynomials, we derive several difference equations satisfied by the recurrence coefficients of these orthogonal polynomials. We also derive differential-difference equations and second order linear ordinary differential equations satisfied by these orthogonal polynomials.

• East Asian mathematical journal
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• v.36 no.1
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• pp.13-24
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• 2020

The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius-Genocchi numbers and polynomials of order α and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations. We also obtain integral representations, implicit and explicit formulas and relations for these polynomials and numbers. Furthermore, we consider some relationships for Apostol type (p, q)-Frobenius-Genocchi polynomials of order α associated with (p, q)-Apostol Bernoulli polynomials, (p, q)-Apostol Euler polynomials and (p, q)-Apostol Genocchi polynomials.

• Journal of applied mathematics & informatics
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• v.37 no.3_4
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• pp.295-305
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• 2019

In the present paper, we introduce (p, q)-Frobenius-Genocchi numbers and polynomials and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, implicit and explicit formulas and relations for these polynomials and numbers. We consider some relationships for (p, q)-Frobenius-Genocchi polynomials of order ${\alpha}$ associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials.