• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.691-696
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• 2000

Very recently Professor Exton derived an interesting hypergeometric generating relation. The authors aim at deriving another hypergeometric generating relation by using the same technique developed by Exton. Some interesting special cases have also been given.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1909-1920
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• 2018

In the paper, the authors find a common solution to three series of differential equations related to the generating function of the Bernoulli numbers of the second kind and present a recurrence relation, an explicit formula in terms of the Stirling numbers of the first kind, and a determinantal expression for the Bernoulli numbers of the second kind.

• 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.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1067-1082
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• 2013

In this paper, we will find some recurrence relations of classical multiple OPS between the same family with different parameters using the generating functions, which are useful to find structure relations and their connection coefficients. In particular, the differential-difference equations of Jacobi-Pineiro polynomials and multiple Bessel polynomials are given.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.4
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• pp.55-63
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• 2001

This paper describes a methodology of product function deployment for understanding product functions and generating systematic functional relation charts. The product function deployment is based on the designer's understanding of product functions. The method involves following steps: 1) definition of product primary function and flows of energy, material, and information, 2) construction of a product tree using key parts, 3) definition of functions and interactions of the functional units, 4) construction of 'from-to' relation matrices, 5) grouping of the parts, and 6) construction of functional relation charts. With this approach, functional relation charts can be generated such that complex product functions are easily understood. The functional relation chart of a refrigerator is generated as an example.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.191-200
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• 2015

Generating functions play an important role in the investigation of various useful properties of the sequences which they generate. Exton [13] presented a very general double generating relation involving products of two Laguerre polynomials. Motivated essentially by Exton's derivation [13], the authors aim to show how one can obtain nineteen new generating relations associated with products of two Laguerre polynomials in the form of a single result. We also consider some interesting and potentially useful special cases of our main findings.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.443-462
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• 2014

Using a simple recurrence relation, we give a new method to compute the Jones polynomials of closed braids: we find a general expansion formula and a rational generating function for the Jones polynomials. The method is used to estimate the degree of the Jones polynomials for some families of braids and to obtain general qualitative results.

• Honam Mathematical Journal
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• v.46 no.1
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• pp.136-145
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• 2024

In this paper we obtained several properties that the characteristic polynomial of the unit-primitive matrix satisfies. In addition, using these properties we have shown that the recurrence relation given as in the formula (1) is true. In fact, Xin and Zhong ([4]) showed it earlier. However, we provide a simpler method here.

• Proceedings of the KIEE Conference
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• 2000.07c
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• pp.1614-1616
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• 2000

The purpose of this study is to manufacture and test a thermoelectric generator which converts unused energy from close-at-hand sources, such as garbage incineration heat and industrial exhaust, to electricity. A manufacturing process and the properties of a thermoelectric generator are discussed before simulating the thermal stress and thermal properties of a thermoelectric module located between an aluminum tube and alumina plate. We can design the thermoelectric modules having the good properties of thermoelectric generation. Resistivity of thermoelectric module for thermoelectric generation consisting of 62 cells was $0.15{\sim}0.4{\Omega}$. The maximum power of thermoelectric generator using thermoelectric generating modules can be defined as temperature function, and in this case it can be analogized the linear relation between current and voltage characteristics as function of temperature. The thermoelectric generator using 128 generating modules was assembled with 4 parallel connected modules sets composed with 32 directly connected modules.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.1033-1048
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• 2020

We synthesize the recent work done on conditionally defined Lucas and Fibonacci numbers, tying together various definitions and results generalizing the linear recurrence relation. Allowing for any initial conditions, we determine the generating function and a Binet-like formula for the general sequence, in both the positive and negative directions, as well as relations among various sequence pairs. We also determine conditions for periodicity of these sequences and graph some recurrent figures in Python.