• 대한수학회논문집
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• 제12권2호
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• pp.203-210
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• 1997

We give some interesting identities involving the Hurwitz and Riemann zeta functions.

• East Asian mathematical journal
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• 제18권2호
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• pp.219-224
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• 2002

Recently the theory of the multiple Gamma functions, which were studied by Barnes and others a century ago, has been revived in the study of determinants of Laplacians. Here we are aiming at evaluating the values of the multiple Gamma functions ${\Gamma}_n(\frac{1}{2})$ in terms of the Hurwitz or Riemann Zeta functions.

• 호남수학학술지
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• 제35권4호
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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 ${\psi}(1+z)$.

• Korean Journal of Mathematics
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• 제19권2호
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• pp.129-147
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• 2011

In this paper we discuss the zeta-determinants of harmonic oscillators having general quadratic potentials defined on $\mathbb{R}^2$. By using change of variables we reduce the harmonic oscillators having general quadratic potentials to the standard harmonic oscillators and compute their spectra and eigenfunctions. We then discuss their zeta functions and zeta-determinants. In some special cases we compute the zeta-determinants of harmonic oscillators concretely by using the Riemann zeta function, Hurwitz zeta function and Gamma function.

• 대한수학회논문집
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• 제17권1호
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• pp.165-173
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• 2002

We first review Ramaswami's find Apostol's identities involving the Zeta function in a rather detailed manner. We then present corrected, or generalized formulas, or a different method of proof for some of them. We also give closed-form evaluation of some series involving the Riemann Zeta function by an integral representation of ζ(s) and Apostol's identities given here.

• East Asian mathematical journal
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• 제21권1호
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• pp.77-103
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• 2005

The theory of multiple Gamma functions was studied in about 1900 and has, recently, been revived in the study of determinants of Laplacians. There is a class of mathematical constants involved naturally in the multiple Gamma functions. Here we summarize those mathematical constants associated with the Gamma and multiple Gamma functions and will show how they are involved, if possible.

• 호남수학학술지
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• 제35권2호
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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.

• 대한수학회논문집
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• 제16권2호
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• pp.319-332
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• 2001

The main object of this paper is first to give tow contiguous analogues of a well-known hypergeometric summation formula for $_2$F$_1$(1/2). We then apply each of these analogues with a view to evaluating the sums of several classes of series in terms of Psi(or Digamma) and the Zeta functions. Relevant connections of the series identities presented here with those given elsewhere are also pointed out.

• 대한수학회보
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• 제61권4호
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• pp.1033-1051
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• 2024

In this paper, we define a parametric variant of generalized Euler sums and construct contour integration to give some explicit evaluations of these parametric Euler sums. In particular, we establish several explicit formulas of (Hurwitz) zeta functions, linear and quadratic parametric Euler sums. Furthermore, we also give an explicit evaluation of alternating double zeta values ${\zeta}({\bar{2j}};\,2m+1)$ in terms of a combination of alternating Riemann zeta values by using the parametric Euler sums.

• East Asian mathematical journal
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• 제31권1호
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• pp.41-53
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• 2015

A large number of series and integral representations for the Stieltjes constants (or generalized Euler-Mascheroni constants) ${\gamma}_k$ and the generalized Stieltjes constants ${\gamma}_k(a)$ have been investigated. Here we aim at presenting certain integral representations for the generalized Stieltjes constants ${\gamma}_k(a)$ by choosing to use four known integral representations for the generalized zeta function ${\zeta}(s,a)$. As a by-product, our main results are easily seen to specialize to yield those corresponding integral representations for the Stieltjes constants ${\gamma}_k$. Some relevant connections of certain special cases of our results presented here with those in earlier works are also pointed out.