• 대한수학회논문집
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• 제32권3호
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• pp.677-688
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• 2017

The composition of Jacobi type finite classes of the classical orthogonal polynomials with two generalized Riemann-Liouville fractional derivatives are considered. The outcomes are expressed in terms of generalized Wright function or generalized hypergeometric function. Similar composition formulas are also obtained by considering the generalized Riemann-Liouville and $Erd{\acute{e}}yi-Kober$ fractional integral operators.

• 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.

• 대한수학회지
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• 제34권4호
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• pp.973-1008
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• 1997

We reconsider the problem of calssifying all classical orthogonal polynomial sequences which are solutions to a second-order differential equation of the form $$ \ell_2(x)y"(x) + \ell_1(x)y'(x) = \lambda_n y(x). $$ We first obtain new (algebraic) necessary and sufficient conditions on the coefficients $\ell_1(x)$ and $\ell_2(x)$ for the above differential equation to have orthogonal polynomial solutions. Using this result, we then obtain a complete classification of all classical orthogonal polynomials : up to a real linear change of variable, there are the six distinct orthogonal polynomial sets of Jacobi, Bessel, Laguerre, Hermite, twisted Hermite, and twisted Jacobi.cobi.

• East Asian mathematical journal
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• 제40권1호
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• pp.25-36
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• 2024

Full univariate moment problems have been studied using continued fractions, orthogonal polynomials, spectral measures, and so on. On the other hand, the truncated moment problem has been mainly studied through confirming the existence of the extension of the moment matrix. A few articles on the multivariate moment problem implicitly presented about some results of this note, but we would like to rearrange the important results for the existence of a representing measure of a moment sequence. In addition, new techniques with orthogonal polynomials will be introduced to expand the means of studying truncated moment problems.

• 대한수학회논문집
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• 제12권4호
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• pp.935-950
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• 1997

When $\tau$ is a quasi-definite moment functional on P, the vector space of all real polynomials, we consider a symmetric bilinear form $\phi(\cdot,\cdot)$ on $P \times P$ defined by $$ \phi(p,q) = \lambad p(a)q(a) + \mu p(b)q(b) + <\tau,p'q'>, $$ where $\lambda,\mu,a$, and b are real numbers. We first find a necessary and sufficient condition for $\phi(\cdot,\cdot)$ and show that such orthogonal polynomials satisfy a fifth order differential equation with polynomial coefficients.

• Computers and Concrete
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• 제5권5호
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• pp.449-459
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• 2008

This paper focuses on the application of two dimensional orthogonal polynomials in the regression analysis for the relationship of product parameters viz. compressive strength, bulk density and water absorption of fly ash cement bricks with other process parameters such as percentages of fly ash, sand and cement. The method has been validated by linear and non-linear two parameter regression models. The use of two dimensional orthogonal system makes the analysis computationally efficient, simple and straight forward. Corresponding co-efficient of determination and F-test are also reported to show the efficacy and reliability of the relationships. By applying the evolved relationships, the product parameters of fly ash cement bricks may be approximated for the use in construction sectors.

• 대한수학회보
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• 제34권1호
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• pp.63-79
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• 1997

Consider an oparator equation of the form : $$ (1.1) H[y](x) = \alpha(x)\delta^2 y(x) + \beta(x)\delta y(x) = \lambda_n y(x), $$ where $\alphs(x)$ and $\beta(x)$ are polynomials of degree at most two and one respectively, $\lambda_n$ is the eigenvalue parameter, and $\delta$ is Hahn's operator $$ (1.2) \delta f(x) = \frac{(q - 1)x + \omega}{f(qx + \omega) - f(x)}, $$ for real constants $q(\neq \pm 1)$ and $\omega$.

• Kyungpook Mathematical Journal
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• 제12권1호
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• pp.115-117
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• 1972

The purpose of the present paper is to evaluate certain integrals involving Laguerre, Jacobi and Hermite polynomials. These integrals are very useful in case of expansion of any polynomial in a series of Orthogonal polynomials [1, Theo. 56].

• 조명전기설비학회논문지
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• 제16권2호
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• pp.98-103
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• 2002

전력수요를 예측할 경우 가장 중요한 문제 중의 하나가 특수일 부하의 처리문제이다. 따라서 본 연구에서 길고(구정, 추석) 짧은(식목일, 현충일 등) 특수일 피크 부하를 신경회로망과 회귀모형을 이용하여 예측하는 방법을 제시한다. 신경회로망 모형의 특수일 부하 처리는 패턴 변환비를 이용하며, 4차의 직교 다항 회귀모형은 과거의 10년 (1985∼1994)간의 특수일 피크부하 자료를 이용하여 길고 짧은 특수일 부하를 예측한다. 특수일 피크 부하를 예측한 결과, 신경회로망 모형의 주간 평균 예측 오차율과 직교 다항 회귀모형의 예측 오차율을 분석한 결과 1∼2[%]대로 두 모형 모두 양호한 결과를 얻었다. 또한 4차의 직교 다항 회귀 모형의 수정결정계수 및 F 검정을 분석한 결과 구성한 예측 모형의 타당성을 확인하였다. 두 모형의 특수일 부하를 예측한 결과를 비교해 보면 긴 특수일 부하를 예측할 때는 패턴 변환비를 이용한 신경회로망 모형이 보다 더 효과적이었고, 짧은 특수일 부하를 예측할 경우에는 두 방법 모두 유효하였다.

• 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.