• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.455-464
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• 2012

In the previous paper [8], the author gave a determinant formula of relative zeta function for cyclotomic function fields. Our purpose of this paper is to extend this result for more general function fields. As an application of our formula, we will give determinant formulas of class numbers for constant field extensions.

• Journal of the Korean School Mathematics Society
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• v.1 no.1
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• pp.151-163
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• 1998

In mathematics education, teaching-learning activity can be divided largely into the understanding the mathematical concepts, derivation of principles and laws, acquirement of the mathematical abilities. We utilize various media, teaching tools, audio-visual materials, manufacturing materials for understanding mathematical concepts. But sometimes we cannot define or explain correctly the concepts as well as the derivation of principles and laws by these materials. In order to solve the problem we can use the computer. In this paper, character and movement state of various quadratic function graph types can be used. Using the computers is more visible than other educational instruments like blackboards, O.H.Ps., etc. Then, students understand the mathematical concepts and the correct quadratic function graph correctly. Consquently more effective teaching-learning activity can be done. Usage of computers is the best method for improving the mathematical abilities because computers have functions of the immediate reaction, operation, reference and deduction. One of the important characters of mathematics is accuracy, so we use computers for improving mathematical abilities. This paper is about the program focused on the part of "the quadratic function graph", which exists in mathematical curriculum the middle school. When this program is used for students, it is expected the following educational effect. 1, Students will have positive thought by arousing interests of learning because this program is composed of pictures, animations with effectiveness of sound. 2. This program will cause students to form the mathematical concepts correctly. 3. By visualizing the process of drawing the quadratic function graph, students understand the quadratic function graph structually. 4. Through the feedback, the recognition ability of the trigonometric function can be improved. 5. It is possible to change the teacher-centered instruction into the student-centered instruction. For the purpose of increasing the efficiencies and qualities of mathmatics education, we have to seek the various learning-teaching methods. But considering that no computer can replace the teacher′s role, tearchers have to use the CIA program carefully.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.467-480
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• 2009

In 1859, Bernhard Riemann, in his epoch-making memoir, extended the Euler zeta function $\zeta$(s) (s > 1; $s{\in}\mathbb{R}$) to the Riemann zeta function $\zeta$(s) ($\Re$(s) > 1; $s{\in}\mathbb{C}$) to investigate the pattern of the primes. Sine the time of Euler and then Riemann, the Riemann zeta function $\zeta$(s) has involved and appeared in a variety of mathematical research subjects as well as the function itself has been being broadly and deeply researched. Among those things, we choose to make a further investigation of the following subjects: Evaluation of $\zeta$(2k) ($k {\in}\mathbb{N}$); Approximate functional equations for $\zeta$(s); Series involving the Riemann zeta function.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.313-334
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• 2024

In the current study, our aim is to define new generalized extended beta and hypergeometric types of functions. Next, we methodically determine several integral representations, Mellin transforms, summation formulas, and recurrence relations. Moreover, we provide log-convexity, Turán type inequality for the generalized extended beta function and differentiation formulas, transformation formulas, differential and difference relations for the generalized extended hypergeometric type functions. Also, we additionally suggest a generating function. Further, we provide the generalized extended beta distribution by making use of the generalized extended beta function as an application to statistics and obtaining variance, coefficient of variation, moment generating function, characteristic function, cumulative distribution function, and cumulative distribution function's complement.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.179-190
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• 2005

We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from standard diffusion equation by replacing the second-order space derivative with a Caputo (or Riemann-Liouville) derivative of order ${\beta}{\in}$ (0, 2] and the first-order time derivative with Caputo derivative of order ${\beta}{\in}$ (0, 1]. The fundamental solution (Green function) for the Cauchy problem is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. We derive explicit expression of the Green function. The Green function also can be interpreted as a spatial probability density function evolving in time. We further explain the similarity property by discussing the scale-invariance of the space-time fractional diffusion equation.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.423-429
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• 2015

Dirichlet series is a Riemann zeta function attached with an arithmetic function. Here, we studied the properties of Dirichlet series and found some identities between arithmetic functions.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.717-734
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• 1996

For a scalar rational function, the spectral data consisting of zeros and poles with their respective multiplicities uniquely determines the function up to a nonzero multiplicative factor. But due to the richness of the spectral structure of a rational matrix function, reconstruction of a rational matrix function from a given spectral data is not that simple.

• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.631-634
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• 2008

In this paper, the parabola will be characterized as the plane curve whose curvature function and support function satisfy a condition, where we define the support function as the distance from origin to the tangent line.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.705-714
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• 2021

The Whittaker function and its diverse extensions have been actively investigated. Here we aim to introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function 𝚽_p,v and investigate some of its formulas such as integral representations, a transformation formula, Mellin transform, and a differential formula. Some special cases of our results are also considered.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.357-385
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• 2014

Recently several authors have extended the Gamma function, Beta function, the hypergeometric function, and the confluent hypergeometric function by using their integral representations and provided many interesting properties of their extended functions. Here we aim at giving further extensions of the abovementioned extended functions and investigating various formulas for the further extended functions in a systematic manner. Moreover, our extension of the Beta function is shown to be applied to Statistics and also our extensions find some connections with other special functions and polynomials such as Laguerre polynomials, Macdonald and Whittaker functions.