• Kyungpook Mathematical Journal
• /
• v.49 no.2
• /
• pp.313-319
• /
• 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.

• The Mathematical Education
• /
• v.40 no.1
• /
• pp.113-123
• /
• 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.

• Journal of the Korean School Mathematics Society
• /
• v.11 no.2
• /
• pp.249-283
• /
• 2008

The purpose of the study was to investigate the definitions and concept images of Infinity and limits for high school students. In addition, the error patterns of the students were also investigated. The participants were 121 girls highschool students and survey method was used to co11ed data. Only 11 % and 5% of the participants revealed the definitions similar to the standard textbook definitions in limits of infinite sequences and infinite series respectively. The participants showed 6 types of error patterns and had more difficulties in understanding and applying concepts and properties of infinite series than those of infinite sequences.

• Communications of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.63-81
• /
• 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
• /
• v.73 no.10
• /
• pp.1512-1518
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.3
• /
• pp.837-849
• /
• 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
• /
• v.16 no.2
• /
• pp.219-223
• /
• 1976

• Kyungpook Mathematical Journal
• /
• v.21 no.2
• /
• pp.225-234
• /
• 1981

• Bulletin of the Korean Mathematical Society
• /
• v.29 no.2
• /
• pp.215-220
• /
• 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.

• Honam Mathematical Journal
• /
• v.41 no.3
• /
• pp.661-666
• /
• 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 $_2F_1$.