• Korean Management Science Review
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• v.14 no.2
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• pp.63-68
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• 1997

Limiting probability in the steady state of regenerative process is one of the most useful characteristics. The formula for this limiting probability in the steady state of the regenerative process is presented in this paper. Because this formula is for the general model, it can be applied to many special systems including 2-unit redundant system. An example for this formula is also presented.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.75-92
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• 2004

A generalised integration by parts formula for sequences of absolutely continuous functions that satisfy the ${\omega}-Appell$ condition and different estimates for the remainder are provided. Applications for particular instances of such sequences are pointed out as well.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.463-474
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• 2001

We find Rodrigues type formula for multi-variate orthogonal polynomial solutions of second order partial differential equations.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.689-694
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• 2014

We find an asymptotic formula of the sum of multi-plicative functions with Dirichlet inversion formula.

• East Asian mathematical journal
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• v.14 no.2
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• pp.321-327
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• 1998

There have been various proofs of the Legendre duplication formula for the Gamma function. Another proof of the formula is given here and a brief history of the Gamma function is also provided.

• East Asian mathematical journal
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• v.27 no.3
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• pp.339-348
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• 2011

B. C. Berndt [6] has evaluated the transformation formula for a large class of functions that includes and generalizes the classical Dedekind eta-function. In this paper, we consider a twisted version of his formula. Using this transformation formula, we derive modular trans-formation formulas for the generating functions for cranks which were central to deduce K. Mahlburg's results in [11].

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.255-280
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• 2008

We derive a formula for the colored Jones polynomial of 2-bridge knots. For a twist knot, a more explicit formula is given and it leads to a relation between the degree of the colored Jones polynomial and the crossing number.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.45-52
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• 1998

In this paper, we establish the exponential formula for C-semigroup. If A is the generator of a C-semigroup S(t), then S(t) can be represented by exp(tA) in some sense.

• Communications of the Korean Mathematical Society
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• v.20 no.2
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• pp.231-238
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• 2005

In this paper, we study the arithmetic properties of orders in a quaternion algebra over a dyadic local field and we find the mass formula of orders.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.4
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• pp.277-295
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• 2022

The author proved a modular transformation formula for a function related to generalized non-holomorphic Eisenstein series and, using this formula, established a lot of infinite series identities. In this paper, we find more generalized series relations which contain the author's previous work.