• East Asian mathematical journal
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• v.18 no.2
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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.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.531-542
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• 2014

Recently, Srivastava et al. [18] introduced the incomplete Pochhammer symbol and studied some fundamental properties and characteristics of a family of potentially useful incomplete hypergeometric functions. Here we introduce the incomplete Lauricella function ${\gamma}_D^{(n)}$ and ${\Gamma}_D^{(n)}$ of n variables, and investigate certain properties of the incomplete Lauricella functions, for example, their various integral representations, differential formula and recurrence relation, in a rather systematic manner. Some interesting special cases of our main results are also considered.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.143-155
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• 2018

In this present paper, our aim is to introduce an extended Wright-Bessel function $J^{{\lambda},{\gamma},c}_{{\alpha},q}(z)$ which is established with the help of the extended beta function. Also, we investigate certain integral transforms and generalized integration formulas for the newly defined extended Wright-Bessel function $J^{{\lambda},{\gamma},c}_{{\alpha},q}(z)$ and the obtained results are expressed in terms of Fox-Wright function. Some interesting special cases involving an extended Mittag-Leffler functions are deduced.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.133-147
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• 2021

Our aim in this paper is to derive several new monotonicity properties and functional inequalities of some functions involving the q-gamma, q-digamma and q-polygamma functions. More precisely, some classes of functions involving the q-gamma function are proved to be logarithmically completely monotonic and a class of functions involving the q-digamma function is showed to be completely monotonic. As applications of these, we offer upper and lower bounds for this special functions and new sharp upper and lower bounds for the q-analogue harmonic number harmonic are derived. Moreover, a number of two-sided exponential bounding inequalities are given for the q-digamma function and two-sided exponential bounding inequalities are then obtained for the q-tetragamma function.

• Journal of Nutrition and Health
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• v.31 no.1
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• pp.28-35
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• 1998

This study was done to investigate the relationship between ultrasonograph fat density (ULFD) using objective measurement and serum enzymes for testing liver function in 101 healthy adults(43 males and 58 females). Average serum enzyme activities in males and females were GOT27.111U/L and 22.46IU/L, GPT 34.06IU/L and 18.501U/L, and ${\gamma}$-GTP 37.67IU/L and 17.201U/L, respectively. Males showed significantly higher activities of GPT and ${\gamma}$-GTP than females. ULFD of the obese group (BMI$\geq$25) was significantly higher than that of the nonobese group. GOT, GPT, and ${\gamma}$-GTP tended to be high in the obese group. GPT and ${\gamma}$-GTP of the high TG group (TG$\geq$170) tended to be markedly high for males, but not for females. GPT was positively correlated with ULFD, body weight , and weight-to-height, ratio, and ${\gamma}$-GTP was positively correlated with body weight, weight-to-height ratio. BNI, and KI. ULFD and ${\gamma}$-GTP were positively correlated with serum TG. These results suggests that , among serum enzymes for testing liver function, GPT has a close relationship with ULFD using objective measurement, while GOT does not. Also , ${\gamma}$-GTP has a close relationship with parameters for obesity.

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.93-106
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• 2005

In this paper, we obtain the generalization of the Hyers-Ulam-Rassias stability in the sense of Gavruta and Ger of the generalized G-type functional equations of the form $f({{\varphi}(x)) = {\Gamma}(x)f(x)$. As a consequence in the cases ${\varphi}(x) := x+p:= x+1$, we obtain the stability theorem of G-functional equation : the reciprocal functional equation of the double gamma function.

• Structural Engineering and Mechanics
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• v.70 no.1
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• pp.1-11
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• 2019

This study deals with a method based on the modified bivariate gamma function for reconstructions of dynamic behavior of delaminated composite plates subjected to impact loads. The proposed bivariate gamma function is associated with micro-genetic algorithms, which is capable of solving inverse problems to determine the stiffness reduction associated with delamination. From computing the unknown parameters, it is possible for the entire dynamic response data to develop a prediction model of the dynamic response through a regression analysis based on the measurement data. The validity of the proposed method was verified by comparing with results employing a higher-order finite element model. Parametric results revealed that the proposed method can reconstruct dynamic responses and the stiffness reduction of delaminated composite plates can be investigated for different measurements and loading locations.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.139-145
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• 1996

We show how some interesting results involving series summation and the digamma function are established by means of Riemann-Liouville operator of fractional calculus. We derive the relation $$ \frac{\Gamma(\lambda)}{\Gamma(\nu)} \sum^{\infty}_{n=1}{\frac{\Gamma(\nu+n)}{n\Gamma(\lambda+n)}_{p+2}F_{p+1}(a_1, \cdots, a_{p+1},\lambda + n; x/a)} = \sum^{\infty}_{k=0}{\frac{(a_1)_k \cdots (a_{(p+1)}{(b_1)_k \cdots (b_p)_k K!} (\frac{x}{a})^k [\psi(\lambda + k) - \psi(\lambda - \nu + k)]}, Re(\lambda) > Re(\nu) \geq 0 $$ and explain some special cases.

• 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.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.18 no.3
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• pp.259-263
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• 2005

The changes in secondary electron emission coefficient(${\gamma}$) and work function($\Phi$$_{\omega}$) have been studied on the surface of MgO protective layer aster plasma(Ar. $O_2$) treatment using ${\gamma}$-focused ion beam (${\gamma}$-FIB) system. The values of ${\gamma}$ varied as follows: $O_2$-treated MgO > Ar-treated MgO > Non-treated MgO, and the work functions varied in the reverse order. The result indicates that both the physical etching and the chemical reaction of $O_2$-plasma removed the contaminating materials from the surface of MgO.