• Kyungpook Mathematical Journal
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• 제49권2호
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• pp.313-319
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• 2009

In the present paper, a theorem dealing with local property of ${\mid}\;\overline{N},p_n,{\theta}_n\;{\mid}_k$ summability of factored Fourier series which generalizes a result of Mazhar [8], has been proved. Some new results have also been obtained.

• 한국수학교육학회지시리즈A:수학교육
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• 제40권1호
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• pp.113-123
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• 2001

We investigated an irrational constant e and compared its computational methods using spreadsheet. Such methods are based on classical definition, infinite series, continued fraction, infinite product exponential function and accelerated classical method. This kind of work is focused on experimental mathematics using computers in math class. This approach will be helpful for mathematics teachers to teach constant e in their classroom.

• 한국학교수학회논문집
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• 제11권2호
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• pp.249-283
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• 2008

본 연구의 목적은 고등학생들이 가지고 있는 극한에 대한 개념 정의와 개념 이미지를 조사해보고 어떤 부적절한 개념 이미지를 가지고 있는지 알아보는데 있다. 또한 관련 개념에 대한 문제를 해결하는 과정에서 어떤 오류를 범하는지도 알아보았다. 연구대상은 인문계 고등학교 이공계열 여학생 121명 이었으며 연구방법은 질문지 검사를 통하여 이루어졌다. 무한수열의 극한의 경우 11%, 무한급수의 경우에는 5%의 학생만이 교과서의 형식적 정의와 유사한 개념정의를 가지고 있었다. 학생들이 보여준 오류유형은 모두 6가지로 나타났으며 학생들은 문제를 푸는 과정에서 무한수열의 극한에 비하여 무한급수의 합에 대한 정의와 성질들을 이해하고 적용하는 것을 더 어려워했다.

• 대한수학회논문집
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• 제35권1호
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• pp.63-81
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• 2020

In this paper we consider certain classes of generalized level 2 Eisenstein series by simple differential calculations of trigonometric functions. In particular, we give four new transformation formulas for some level 2 Eisenstein series. We can find that these level 2 Eisenstein series are reducible to infinite series involving hyperbolic functions. Moreover, some interesting new examples are given.

• Journal of the Korean Physical Society
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• 제73권10호
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• pp.1512-1518
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• 2018

The problem of scalar wave scattering by a sphere on or near a planar substrate is analytically solved. The solution is a set of wave functions coming in the form of infinite series of spherical and plane waves. In air, the incident plane wave is either scattered by the sphere or reflected from the substrate. A part of these scattered or reflected waves propagate to the other object where it is reflected and scattered again. Such processes of scattering and reflection repeat in turn indefinitely to generate multiply scattered waves, which are represented in the corresponding terms in the infinite series. The term in the series can be arranged in a recognizable manner to explicitly reveal the involved process and the multiplicity of scattering.

• 대한수학회보
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• 제55권3호
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• pp.837-849
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• 2018

In this paper, we study the closedness such as seminomality and t-closedness, and Noetherian-like properties such as piecewise Noetherianness and Noetherian spectrum, of Hurwitz polynomial rings and Hurwitz series rings. To do so, we construct an isomorphism between a Hurwitz polynomial ring (resp., a Hurwitz series ring) and a factor ring of a polynomial ring (resp., a power series ring) in a countably infinite number of indeterminates.

• Kyungpook Mathematical Journal
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• 제16권2호
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• pp.219-223
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• 1976

• Kyungpook Mathematical Journal
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• 제21권2호
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• pp.225-234
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• 1981

• 대한수학회보
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• 제29권2호
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• pp.215-220
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• 1992

Using a matrix method, pp. Antosik and C. Swartz have obtained a series of nice properties of bounded multiplier convergent (BMC) series on metric linear spaces ([1],[8],[9]). In this paper, we establish a basic property of BMC series on topological vector spaces which is a generalization of a result due to J. Batt([2], Th.2). From this, we have obtained a kind of inclusion theorem of operator spaces. This theorem yields a nice result on infinite systems of linear equations.

• 호남수학학술지
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• 제41권3호
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• pp.661-666
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• 2019

In this short research note, we aim to provide a new proof of classical Dixon's summation theorem for the series $_3F_2$ with unit argument. The theorem is obtained by evaluating an infinite integral and making use of classical Gauss's and Kummer's summation theorem for the series $_2F_1$.