• Korean Journal of Mathematics
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• 제16권1호
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• pp.51-55
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• 2008

Let f be an analytic function with a simple zero in the reals or the complex numbers. An extraneous fixed-point of an iteration function is a fixed-point different from a zero of f. We prove that all extraneous fixed-points of Laguerre-like iteration functions and general Laguerre-like functions are repulsive.

• 대한수학회논문집
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• 제33권3호
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• pp.1013-1024
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• 2018

The main object of this paper is to set up two (conceivably) valuable double integrals including the multiplication of Bessel function with Jacobi and Laguerre polynomials, which are given in terms of Srivastava and Daoust functions. By virtue of the most broad nature of the function included therein, our primary findings are equipped for yielding an extensive number of (presumably new) fascinating and helpful results involving orthogonal polynomials, Whittaker functions, sine and cosine functions.

• 대한수학회논문집
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• 제30권3호
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• pp.191-200
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• 2015

Generating functions play an important role in the investigation of various useful properties of the sequences which they generate. Exton [13] presented a very general double generating relation involving products of two Laguerre polynomials. Motivated essentially by Exton's derivation [13], the authors aim to show how one can obtain nineteen new generating relations associated with products of two Laguerre polynomials in the form of a single result. We also consider some interesting and potentially useful special cases of our main findings.

• 조명전기설비학회논문지
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• 제29권2호
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• pp.40-46
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• 2015

This paper presents a method of controlling a three-phase VSI (Voltage Source Inverter) using MPC (Model Predictive Control) designed using Laguerre functions. It also provides a model of the three-phase VSI and its resistive-inductive load and then an overview of MPC design using Laguerre functions. The biggest challenge in using MPC is the high number of computations involved, which makes online implementation difficult. On the other hand, the LMPC (Laguerre Model Predictive Control) reduces the number of computations made and so online implementation becomes possible where traditional MPC would be unteneble. The simulation results from MATLAB are also provided.

• 대한수학회논문집
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• 제36권2호
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• pp.299-312
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• 2021

The main aim of this paper is to introduce and study the generalized Laguerre polynomials and prove that these polynomials are characterized by the generalized hypergeometric function. Also we investigate some properties and formulas for these polynomials such as explicit representations, generating functions, recurrence relations, differential equation, Rodrigues formula, and orthogonality.

• 호남수학학술지
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• 제43권1호
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• pp.141-151
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• 2021

The main object of the present paper is to introduce the generalized Laguerre matrix polynomials for two variables. We prove that these matrix polynomials are characterized by the generalized hypergeometric matrix function. An explicit representation, generating functions and some recurrence relations are obtained here. Moreover, these matrix polynomials appear as solution of a differential equation.

• 대한수학회논문집
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• 제27권4호
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• pp.721-732
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• 2012

The principal aim of the paper is to investigate new integral expression $${\int}_0^{\infty}x^{s+1}e^{-{\sigma}x^2}L_m^{(\gamma,\delta)}\;({\zeta};{\sigma}x^2)\;L_n^{(\alpha,\beta)}\;({\xi};{\sigma}x^2)\;J_s\;(xy)\;dx$$, where $y$ is a positive real number; $\sigma$, $\zeta$ and $\xi$ are complex numbers with positive real parts; $s$, $\alpha$, $\beta$, $\gamma$ and $\delta$ are complex numbers whose real parts are greater than -1; $J_n(x)$ is Bessel function and $L_n^{(\alpha,\beta)}$ (${\gamma};x$) is generalized Laguerre polynomials. Some integral formulas have been obtained. The Maple implementation has also been examined.

• 대한수학회논문집
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• 제33권2호
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• pp.619-630
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• 2018

In this paper, we obtain a (p, q)-extension of the Whittaker function $M_{k,{\mu}}(z)$ together with its integral representations, by using the extended confluent hypergeometric function of the first kind ${\Phi}_{p,q}(b;c;z)$ [recently extended by J. Choi]. Also, we give some of its main properties, namely the summation formula, a transformation formula, a Mellin transform, a differential formula and inequalities. In addition, our extension on Whittaker function finds interesting connection with the Laguerre polynomials.

• 한국통신학회논문지
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• 제39A권3호
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• pp.140-148
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• 2014

본 논문은 전자기파 신호 계산에 있어 하이브리드 방식의 기저 함수로써 Gaussian 함수를 제안하고자 한다. 하이브리드 방식은 전반부 시간 및 낮은 주파수 데이터를 이용하여 후반부 시간 및 높은 주파수 데이터를 구하는 방식이다. 시간을 이용한 MOT, 주파수를 이용한 MOM 방식의 장점만을 가져오기 때문에 전자기 분석 데이터를 구하기 위한 시간이 감소되며 오차가 적다는 장점이 있다. 이를 위해서는 기저 함수를 필요로 하며 Hermite, Laguerre를 기저 함수로 사용한 기존의 방법과의 비교를 통해 제안된 방법의 성능을 확인하였다.

• 대한토목학회논문집
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• 제11권4호
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• pp.91-102
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• 1991

저수지군을 최적으로 운영하려고 할때 일반적으로 동적계획법을 이용하는데 저수지 수의 증가와 변수의 이산화에 따라 계산 용량이 지수적으로 팽창하는 결점을 내포하고 있다. 이 문제를 해결하기 위해서 본 논문에서는 저수지 시스템 변수가 LP(Laguerre Polynomial)로 표현된 새로운 모형 개발을 시도하였다. 새로운 계획모형은 QP(Quadratic Programming) 형태이다. 이 모형의 해는 확장 라그란지안 곱수 방법(Augmented Lagrangian Multiplier Method)의 비선형계획법에 의해서 QP해를 구하였다. 그 결과 저수 수준은 기존의 결과보다 높게 유지하려는 경향을 보였으며, 평가된 편익 값은 다른 방법들과 비슷한 값이었다.