• Journal of applied mathematics & informatics
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• v.41 no.3
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• pp.687-696
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• 2023

In this paper, we introduce the 2-variable mixed-type Hermite polynomials and organize some new symmetric identities for these polynomials. We find induced differential equations to give explicit identities of these polynomials from the generating functions of 2-variable mixed-type Hermite polynomials.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1185-1194
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• 2017

In this paper, we present nonlinear differential equations arising from the generating function of the Eulerian polynomials. In addition, we give explicit formulae for the Eulerian polynomials which are derived from our nonlinear differential equations.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.205-212
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• 2018

In this paper, we study linear differential equations arising from the generating functions of twisted (h, q)-tangent polynomials. We give explicit identities for the twisted (h, q)-tangent polynomials.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.461-473
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• 2022

In this paper, we study differential equations arising from the generating functions of the geometric polynomials. We give explicit identities for the geometric polynomials. Finally, we investigate the zeros of the geometric polynomials by using computer.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.445-454
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• 2011

In this paper, we first find a raising operator and a lowering operator for multiple Bessel polynomials and then give a differential equation having multiple Bessel polynomials as solutions. Thus the differential equations were found for all multiple orthogonal polynomials that are orthogonal with respect to the same type of classical weights introduced by Aptekarev et al.

• Journal of Applied and Pure Mathematics
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• v.4 no.5_6
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• pp.221-231
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• 2022

In this paper, we study differential equations arising from the generating functions of (p, q)-Hermite polynomials. We use this differential equation to give explicit identities for (p, q)-Hermite polynomials.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.869-882
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• 2023

In this paper, we find induced differential equations to give explicit identities of these polynomials from the generating functions of 2-variable mixed-type Hermite polynomials. Moreover, we observe the structure and symmetry of the zeros of the 2-variable mixed-type Hermite equations.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.159-173
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• 2020

In this paper we define a new generalized polynomials of derangements. It also derives the differential equations that occur in the generating function of the generalized polynomials of derangements. We establish some new identities for the generalized polynomials of derangements. Finally, we perform a survey of the distribution of zeros of the generalized polynomials of derangements.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.427-438
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• 2020

In this paper we define a new degenerate Bell-Carlitz polynomials. It also derives the differential equations that occur in the generating function of the degenerate Bell-Carlitz polynomials. We establish some new identities for the degenerate Bell-Carlitz polynomials. Finally, we perform a survey of the distribution of zeros of the degenerate Bell-Carlitz polynomials.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.239-246
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• 2021

In this article, a study of generalized Bateman's matrix polynomials is presented. We obtained partial differential equations by using differential operators in the generalized Bateman's matrix polynomials for two variables. Then we introduced some different recurrence relationships of the generalized Bateman's matrix polynomials. Finally present the relationship between the generalized Bateman's matrix polynomials of one and two variables.