• Honam Mathematical Journal
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• v.45 no.4
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• pp.682-688
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• 2023

The main object of this paper is to establish twenty definite integrals involving Struve functions and modified Srtuve functions associated with hypergeometric functions, which are presumably new and not present in the scientific literature.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.979-990
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• 2017

Inspired by the results obtained by Brychkov ([2]), the authors evaluate a large number of new and interesting double definite integrals. The results are obtained with the use of classical hypergeometric summation theorems and a well-known double finite integral due to Edwards ([3]). The results are given in terms of Psi and Hurwitz zeta functions suitable for numerical computations.

• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.111-117
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• 2021

In this paper we aim to establish a new class of six definite double integrals in terms of gamma functions. The results are obtained with the help of some definite integrals obtained recently by Kim and Edward equality. The results established in this paper are simple, interesting, easily established and may be useful potentially.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.15-20
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• 2002

We present an explicit form for a class of definite integrals whose special cases include some definite integrals evaluated, over a century ago, by Cahen who made use of an appropriate contour integral for the integrand of a well-known integral representation of the Riemann Zeta function given in (3). Furthermore another analogous class of definite integral formulas and some identities involving Riemann Zeta function and Euler numbers En are also obtained as by-products.

• Honam Mathematical Journal
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• v.39 no.3
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• pp.453-463
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• 2017

The aim of this paper is to provide a class of six definite general integrals in terms of gamma function. The results are established with the help of generalized summation formulas obtained earlier by Rakha and Rathie. The results established in this paper are simple, interesting, easily established and may be useful potentially.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.26-34
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• 2021

In this paper two interesting double integrals involving product of two generalized hypergeometric functions have been evaluated in terms of gamma function. The results are derived with the help of known integrals involving hypergeometric functions recorded in the paper of Rathie et al. [6]. We also give several very interesting special cases.

• School Mathematics
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• v.11 no.2
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• pp.301-316
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• 2009

There are two distinct processes, definite integral and indefinite integral, in the integral calculus. And the term 'integral' has two meanings. Most students regard indefinite integrals as definite integrals with indefinite interval. One possible reason is that calculus textbooks do not concern the meaning in the relationship between definite integral and indefinite integral. In this paper we investigated the historical development of concepts of definite integral and indefinite integral, and the relationship between the two. We have drawn pedagogical implication from the result of analysis.

• Communications of Mathematical Education
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• v.36 no.1
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• pp.39-57
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• 2022

This study aims to design an integral instruction method that follows the Abstraction in Context (AiC) framework proposed by Hershkowitz, Schwarz, and Dreyfus to help students in acquiring in-depth understanding of the relationship between indefinite integrals and definite integrals and to analyze how the students' understanding improved as a result. To this end, we implemented lessons according to the integral instruction method designed for eight 11th grade students in a science high school. We recorded and analyzed data from graded student worksheets and transcripts of classroom recordings. Results show that students comprehend three knowledge elements regarding relationship between indefinite integral and definite integral: the instantaneous rate of change of accumulation function, the calculation of a definite integral through an indefinite integral, and The determination of indefinite integral by the accumulation function. The findings suggest that the AiC framework is useful for designing didactical activities for conceptual learning, and the accumulation function can serve as a basis for teaching the three knowledge elements regarding relationship between indefinite integral and definite integral.

• East Asian mathematical journal
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• v.15 no.1
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• pp.111-114
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• 1999

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.545-555
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• 2004

Ever since the time of Euler, the so-called Euler sums have been evaluated in many different ways. We give here a proof of the classical Euler sum by following Lewin's method. We also consider some related formulas involving Euler sums, which are evaluatable from some known definite integrals.