• East Asian mathematical journal
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• v.29 no.5
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• pp.545-550
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• 2013

A remarkably large number of integral formulas have been investigated and developed. Certain large number of integral formulas are expressed as derivatives of some known functions. Here we choose to recall such a formula to present explicit expressions in terms of Gamma function, Psi function and Polygamma functions. Some simple interesting special cases of our main formulas are also considered. It is also pointed out that the same argument can establish explicit integral formulas for other those expressed in terms of derivatives of some known functions.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1155-1161
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• 2014

In this paper, we rederive the identity ${\Gamma}_q(x){\Gamma}_q(1-x)={\frac{{\pi}_q}{sin_q({\pi}_qx)}$. Then, we give q-analogue of Gauss' multiplication formula and study representation of q-oscillator algebra in terms of the q-factorial polynomials.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.239-255
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• 2014

We develop a set of identities for Euler type sums. In particular we investigate products of shifted harmonic numbers of order two and reciprocal binomial coefficients.

• Honam Mathematical Journal
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• v.22 no.1
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• pp.53-60
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• 2000

We evaluate some interesting families of infinite series expressed in terms of the Psi (or Digamma) and Zeta functions by analyzing the well-known identity associated with $_3F_2$ due to Watson. Some special cases are also considered.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.329-342
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• 2016

Motivated essentially by Brychkov's work [1], we evaluate some new integrals involving hypergeometric function and the logarithmic function (including those obtained by Brychkov[1], Choi and Rathie [3]), which are expressed explicitly in terms of Gamma, Psi and Hurwitz zeta functions suitable for numerical computations.

• 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 ${\psi}(1+z)$.

• Communications of the Korean Mathematical Society
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• v.19 no.3
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• pp.545-555
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• 2004

Ever since the time of Euler, the so-called Euler sums have been evaluated in many different ways. We give here a proof of the classical Euler sum by following Lewin's method. We also consider some related formulas involving Euler sums, which are evaluatable from some known definite integrals.

• 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.26 no.3
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• pp.591-599
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• 2013

A large number of sequences of polynomials and numbers have arisen in mathematics. Some of them, for example, Bernoulli polynomials and numbers, have been investigated deeply and widely. Here we aim at presenting certain interesting and (potentially) useful identities involving mainly in the second-order Eulerian numbers and Stirling polynomials, which seem to have not been given so much attention.

• 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.