• Kyungpook Mathematical Journal
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• 제18권2호
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• pp.311-319
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• 1978

This paper deals with the evaluation of two definite integrals involving spheroidal wave function, H-function of two variables, and the generalized hypergeometric function. Also, an expansion formula for the product of generalized hypergeometric function and the H-function of two variables has been obtained. Since the H-function of two variables, spheroidal wave functions, and the generalized hypergeometric function may be transformed into a number of higher transcendental functions and polynomials, the results obtained in this paper include some known results as their particular cases. As an application of such results, a problem of heat conduction in a non-homogenous bar has been solved by using the generalized Legendre transform [9].

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제38권3호
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• pp.443-458
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• 2024

본 연구는 2015 개정 수학과 교육과정에서 정적분을 '미적분학의 기본정리'로 도입하는 것에 대한 수학 학문적 관점과 실제 학교 현장의 현황을 분석하였다. 이에 수학 학문적 관점과 학교 현장의 현황을 조사하기 위해 해석학 전공 교수 12명과 교사 36명을 대상으로 연구를 진행하였다. 수학 학문적 관점에서 해석학 전공 교수들은 2015 개정 수학과 교육과정에서 정적분을 '미적분학의 기본정리'로 도입하는 것이 정적분의 본질과 의미를 유의미하게 나타내기 힘들다고 하였다. 실제 학교 현장에서 교사는 정적분과 도형의 넓이와의 관계에 대한 필요성은 인식하고 있지만 '미적분학의 기본정리'로 정적분을 도입할 경우 학생들은 정적분과 도형의 넓이와의 관련성을 인식하기 어려워한다고 하였다. 이후 시행 될 2022 개정 교육과정에서도 정적분을 '미적분학의 기본정리'로 도입함에 따라 본 연구를 통해 정적분 도입 및 지도에 대한 시사점을 생각해 볼 수 있다. 또한, '미적분학의 기본정리'로 정적분을 도입할 때 정적분을 도형의 넓이와 관련지을 수 있는 효과적인 교수·학습 방법과 다양한 시각적 도구 및 매체에 대한 후속 연구를 제안하였다.

• 대한수학회논문집
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• 제31권2호
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• pp.343-353
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• 2016

A remarkably large number of integrals whose integrands are associated, in particular, with a variety of special functions, for example, the hypergeometric and generalized hypergeometric functions have been recorded. Here we aim at presenting certain (presumably) new and (potentially) useful integral formulas whose integrands are involved in a product of $_2F_1$, Srivastava polynomials, and $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ functions. The main results are derived with the help of some known definite integrals obtained earlier by Qureshi et al. [4]. Some interesting special cases of our main results are also considered.

• 호남수학학술지
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• 제40권1호
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• pp.61-73
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• 2018

The main aim of this research paper is to evaluate the general integral of the form $${\int_{0}^{1}}x^{c-1}(1-x)^{c+{\ell}}[1+{\alpha}x+{\beta}(1-x)]^{-2c-{\ell}-1}\atop {\times}_3F_2\left\[ {a,\;b,\;2c+{\ell}+1} \\ {\frac{1}{2}(a+b+i+1),\;2c+j\;;\frac{(1+{\alpha})x}{1+{\alpha}x+{\beta}(1-x)} }\right]dx$$ in the most general form for any ${\ell}{\in}\mathbb{Z}$; and $i, j=0,{\pm}1,{\pm}2$. The results are established with the help of generalized Watson's summation theorem due to Lavoie, et al. Fifty interesting general integrals have also been obtained as special cases of our main findings.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제4권1호
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• pp.71-76
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• 1997

A new proof of the well-known identity involved in the Beta function B(p, q) is given by using the theory of hypergeometric series and a brief history of Gamma function is also provided. The method here is shown to be able to apply to evaluate some definite integrals.

• 대한수학교육학회지:수학교육학연구
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• 제11권2호
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• pp.307-320
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• 2001

Traditionally, there are many inherent restrictions in highschool mathematics textbooks. They are restricted in its contents and inevitably resorted to reader's ability of intuition. So they are usually lacked logical precisions and have various differences in expressions. We are mainly concerned with the definite integral and its applications in current highschool mathematics II textbooks according to 6th curriculum. We choose 6 of them arbitrarily and survey by comparison to deduce some controversial topics among them as follows. 1) absurd metaphors in formula process 2) confusions in important notations and too much choices in terms and statements. 3) lack of precisions in - teaching hierarchy (between some contents of Physics and the applications of definite integral) - introducing a proof of theorem (fundamental theorem of Calculus I) - introducing the methods (integral substitutions 1, ll) 4) adopting small topics such as - mean value theorem of integral - integrals with variable limits. In coming 7th curriculum, highschool students in Korea are supposed to choose calculus as a whole, independent course. So we hope that the suggested controversial topics are to be referred by authors to improve the preceding Mathematics ll textbooks and for teachers to use them for better mathematics education.

• 한국항해항만학회:학술대회논문집
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• 한국항해항만학회 2000년도 추계학술대회논문집
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• pp.25.2-31
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• 2000

Recently, Fuzzy theory has been applied in evaluation problem. Fuzzy evaluation based on Fuzzy theory can accommodate fuzziness of judgement with people through introducing Fuzzy measure. Representative Fuzzy evaluation is Fuzzy Integral using Fuzzy measure. Definite methodology using Fuzzy Integral HFI(Hierarchical Fuzzy Integrals), HFEA(Hierarchical Fuzzy Evaluation Algorithm), HFP(Hierarchical Fuzzy Process), etc. In this paper, we deal with problem identifying evaluation value using Fuzzy Relation Equation at these Fuzzy evaluation. We verify relation between Input data and Output data through @-operation and apply this to HFP. And that we verify evaluation value which objects of evaluation are able to possess.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1987년도 정기총회 및 창립40주년기념 학술대회 학회본부
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• pp.457-462
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• 1987

This paper deals with the PWM controlled active AC power filter. A new PWM control method from the viewpoint of speed and simplicity is proposed. And a microprocessor-based controller is used to realize the active AC power filter. The existing PWM control methods are primarily based on Fourier series expansion and these methods need FFT calculation and solving nonlinear harmonic equations, which are heavy burden to real-time control. The proposed method is based upon generalized pulse series expansion and needs only definite integrals of harmonic signal. So, computational effort can be reduced by a large margin. The digital circuit using 16-bit microprocessor is designed to implement the actual active power filler.

• East Asian mathematical journal
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• 제32권1호
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• pp.43-46
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• 2016

The Clausen function $Cl_2$(x) arises in several applications. A large number of indefinite integrals of logarithmic or trigonometric functions can be expressed in closed form in terms of $Cl_2$(x). Very recently, Choi and Srivatava [3] and Choi [1] investigated certain integral formulas associated with $Cl_2$(x). In this sequel, we present an interesting new definite integral formula for the Clausen function $Cl_2$(x) by using a known relationship between the Clausen function $Cl_2$(x) and the generalized Zeta function ${\zeta}$(s, a). Also an interesting integral representation for the Catalan constant G is considered as one of two special cases of our main result.

• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.781-795
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• 2020

In this paper, we obtain an analytical solution for an unsolved definite integral RC (m, n) from a 1915 paper of Srinivasa Ramanujan. We obtain our solution using the hypergeometric approach and an infinite series decomposition identity. Also, we give some generalizations of Ramanujan's integral RC (m, n) defined in terms of the ordinary hypergeometric function 2F3 with suitable convergence conditions. Moreover as applications of our result we obtain nine new infinite summation formulas associated with the hypergeometric functions 0F1, 1F2 and 2F3.