• Communications of the Korean Mathematical Society
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• v.22 no.2
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• pp.219-225
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• 2007

Since the time of Euler, the dilogarithm and polylogarithm functions have been studied by many mathematicians who used various notations for the dilogarithm function $Li_2(z)$. These functions are related to many other mathematical functions and have a variety of application. The main objective of this paper is to present corrected versions of two equivalent factorization formulas involving the Legendre's Chi-function $\chi_2$ and an evaluation of a class of integrals which is useful to evaluate some integrals associated with the dilogarithm function.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.467-472
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• 2014

With the properties of Riemann zeta function, we find an asymptotic formula of the sum for the absolute value of M$\ddot{o}$bius function, $\sum_{n{\leq}x}{\mid}{\mu}(n){\mid}$, using Dirichlet inversion formula.

• Korean Journal of Mathematics
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• v.28 no.1
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• pp.123-136
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• 2020

In this paper, we give an explicit formula as a rational function for the Ihara zeta function of every finite connected graph without degree one vertices whose circuit rank is two.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.277-298
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• 2021

In this paper, we propose an extension of the classical Bessel function by means of our ℓ-hypergeometric function [2]. As the main results, the infinite order differential equation, the generating function relation, and contour integral representations including Schläfli's integral analogue are derived. With the aid of these, other results including some inequalities are also obtained. At the end, the graphs of these functions are plotted using the Maple software.

• Research in Mathematical Education
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• v.3 no.1
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• pp.35-56
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• 1999

The evolution of the function concept was delineated in terms of the 17th and 18th Centuries' dependent nature of function, and the 19th and 20th Centuries' arbitrary and univalent nature of function. According to mathematics educators' beliefs about the value of the function concept in school mathematics, certain definitions of the concept tend to be emphasized. This study discusses three types - genetical (dependence), logical (settheoretical), analogical (machine/equations) - of definition of function and their values.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.137-146
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• 2013

Motivated essentially by their potential for applications in a wide range of mathematical and physical problems, the log-sine and log-cosine integrals have been evaluated, in the existing literature on the subject, in many different ways. The main object of this paper is to present explicit evaluations of some families of log-sine and log-cosine integrals by making use of the familiar Beta function.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.117-121
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• 2016

In this paper we give a determinant formula for the ratio of relative congruence zeta functions of cyclotomic function fields.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.849-856
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• 2016

General summation formula for sums involving ${\sigma}(n)/n$ is expressed with infinite series containing a Bessel function.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.435-443
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• 1998

Some mathematical constants have been used in evaluating series involving the Zeta function, the origin of which can be traced back to an over two centries old theorem of Christian Goldbach. We show some of the series involving the Zeta function can be evaluated in terms of the Catalan's constant by using the theory of the double Gamma function.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.1
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• pp.83-88
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• 2015

In this paper we give a determinant formula for the relative congruent zeta function in cyclotomic function fields.