• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.439-447
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• 2015

Very recently the authors have obtained a very interesting reduction formula for the Srivastava's triple hypergeometric series $F^{(3)}$(x, y, z) by applying the so-called Beta integral method to the Henrici's triple product formula for the hypergeometric series. In this sequel, we also present three more interesting reduction formulas for the function $F^{(3)}$(x, y, z) by using the well known identities due to Bailey and Ramanujan. The results established here are simple, easily derived and (potentially) useful.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.23-28
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• 1997

In this paper, we investigate continuity of $$F(x)=(H){\int}_a^x\;fdG$$ and Henstock-Stieltjes integrability of product of two functions and obtain the formula of integration by parts for the Henstock-Stieltjes integral.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.703-715
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• 2006

Recently, we proved the existence theorem of measure-valued Feynman-Kac formula and showed that it satisfied Volterra's integral equation. In this paper, we establish the operational calculus for a measure-valued Dyson series and give some examples related to the measure-valued Dyson series.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.383-390
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• 2019

In this paper, we discuss special polynomials involving exponential distribution, which is related to life testing. We derive some identities of special polynomials such as the symmetric property, recurrence formula and so on. In addition, we investigate explicit properties of special polynomials by using their derivative and integral.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.6 no.2
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• pp.43-52
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• 2002

By the use of Taylor's expansion formula with the integral remainder, an accurate approximation for the fiber refractive index profile is given.

• Journal of the Korean Chemical Society
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• v.17 no.6
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• pp.395-405
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• 1973

By use of an Integral Hellmann-Feynman formula, the cubic crystal field splitting 1O Dq in $KNiF_3$ is calculated from first principles. Numerical values of covalency parameters and necessary integrals are quoted from Sugano and Shulman. The result, 7100$cm^{-1}$, is in excellent agreement with the observed value, 7250$cm^{-1}$. It is found that higher order perturbation energy correction is of the same order of magnitude as 10 Dq itself and is, therefore, essential tin calculating 10 Dq from first principles. It is also found that the point charge potential is the dominant part of the crystal field potential.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.47-53
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• 2017

Generalized integral formulas involving the generalized modified k-Bessel function $J^{b,c,{\gamma},{\lambda}}_{k,{\upsilon}}(z)$ of first kind are expressed in terms generalized Wright functions. Some interesting special cases of the main results are also discussed.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.639-645
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• 2013

We aim at presenting certain integral representations for the Riemann Zeta function ${\zeta}(s)$ at positive integer arguments by using some known integral representations of log ${\Gamma}(1+z)$ and ${\psi}(1+z)$.

• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.499-516
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• 2005

We obtain the type set for the fractional integral operator along the curve $(t,t^2,\;{\alpha}t^3)$ on the three dimensional Heisenberg group when $\alpha\neq{\pm}1/6$. The proof is based on the Fourier inversion formula and the angular Littlewood-Paley decompositions in the Heisenberg group in [5].

• Journal of the Korean Mathematical Society
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• v.43 no.3
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• pp.461-489
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• 2006

In this article, we establish the existence theorem for measure-valued Dyson series and show that it satisfies the Volterra-type integral equation. Furthermore, we prove the stability theorems for measure-valued Dyson series.