• 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.

• 대한수학회논문집
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• 제22권2호
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• pp.219-225
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• 2007

Since the time of Euler, the dilogarithm and polylogarithm functions have been studied by many mathematicians who used various notations for the dilogarithm function $Li_2(z)$. These functions are related to many other mathematical functions and have a variety of application. The main objective of this paper is to present corrected versions of two equivalent factorization formulas involving the Legendre's Chi-function $\chi_2$ and an evaluation of a class of integrals which is useful to evaluate some integrals associated with the dilogarithm function.

• 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.

• 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 ${\psi}(1+z)$.