• 충청수학회지
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• 제31권1호
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• pp.103-130
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• 2018

In the paper we establish some new results depending on the comparative growth properties of composite entire and meromorphic functions using relative $_pL^*-order$, relative $_pL^*-lower$ order and differential monomials, differential polynomials generated by one of the factors.

• 대한수학회보
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• 제58권4호
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• pp.795-814
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• 2021

In this paper, we study the transcendental meromorphic solutions for the nonlinear differential equations: fⁿ + P(f) = R(z)e^α(z) and fⁿ + P_*(f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z) in the complex plane, where P(f) and P_*(f) are differential polynomials in f of degree n - 1 with coefficients being small functions and rational functions respectively, R is a non-vanishing small function of f, α is a nonconstant entire function, p₁, p₂ are non-vanishing rational functions, and α₁, α₂ are nonconstant polynomials. Particularly, we consider the solutions of the second equation when p₁, p₂ are nonzero constants, and deg α₁ = deg α₂ = 1. Our results are improvements and complements of Liao ([9]), and Rong-Xu ([11]), etc., which partially answer a question proposed by Li ([7]).

• Korean Journal of Mathematics
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• 제25권2호
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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.

• 대한수학회보
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• 제56권1호
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• pp.151-167
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• 2019

In this article, a hybrid family of polynomials related to the Appell polynomials is introduced. Certain properties including quasimonomiality, differential equation and determinant definition of these polynomials are established. Further, applications of Carlitz's theorem to these polynomials and to certain other related polynomials are considered. Examples providing the corresponding results for some members belonging to this family are also considered.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.797-802
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• 2005

We generate simplex polynomials by using a method, which produces an OPS in (d + 1) variables from an OPS in d variables and the Jacobi polynomials. Also we obtain a partial differential equation of the form $${\Sigma}_{i,j=1}^{d+1}\;A_ij{\frac{{\partial}^2u}{{\partial}x_i{\partial}x_j}}+{\Sigma}_{i=1}^{d+1}\;B_iu\;=\;{\lambda}u$$, which has simplex polynomials as solutions, where ${\lambda}$ is the eigenvalue parameter.

• Kyungpook Mathematical Journal
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• 제50권2호
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• pp.237-253
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• 2010

It is shown that an appropriate combination of methods, relevant to operational calculus and to special functions, can be a very useful tool to establish and treat a new class of Hermite and Konhauser polynomials. We explore the formal properties of the operational identities to derive a number of properties of the new class of Hermite and Konhauser polynomials and discuss the links with various known polynomials.

• 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.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.787-796
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• 2005

We generalize a characterization of classical orthogonal polynomials and obtain a two-variable analogue. Also an example is given arising from a second order partial differential equation.

• 대한수학회논문집
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• 제35권3호
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• pp.773-787
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• 2020

In this paper we consider the uniqueness of meromorphic functions when two linear differential polynomials share a set of values. Our result improves and rectifies a result of An and Khoai.

• 대한수학회보
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• 제38권3호
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• pp.463-474
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• 2001

We find Rodrigues type formula for multi-variate orthogonal polynomial solutions of second order partial differential equations.