• East Asian mathematical journal
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• v.21 no.1
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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.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.699-709
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• 2014

In the present paper, we investigate starlikeness conditions for q-differential operator by using the concept of quantum calculus in the unit disk.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.523-550
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• 2009

In the paper two-weight inequalities of various type for strong fractional maximal functions and potentials with multiple kernels defined on $\mathbb{R}^2$ are established.

• East Asian mathematical journal
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• v.21 no.1
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• pp.123-135
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• 2005

We have extended the $H^p$ space and estabilished the derivative of inner functions, Blaschke product on weighted Hardy spaces for the unit disc in complex plane.

• Honam Mathematical Journal
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• v.36 no.1
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• pp.55-66
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• 2014

In this paper, we study the convolution sums involving odd divisor functions, and their relations to Weierstrass ${\wp}$-functions.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.475-489
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• 2012

A plateau in a Motzkin path is a sequence of three steps: an up step, a horizontal step, then a down step. We find three different forms for the bivariate generating function for plateaus in Motzkin paths, then generalize to longer plateaus. We conclude by describing a further generalization: a continued fraction form from which one can easily derive new multivariate generating functions for various kinds of path statistics. Several examples of generating functions are given using this technique.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1229-1237
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• 2018

In this paper, we obtain the coefficient bounds for subclass of meromorphic bi-univalent functions by using the Faber polynomial expansions. The results presented in this paper would generalize and improve some recent works.

• Bulletin of the Korean Mathematical Society
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• v.42 no.4
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• pp.889-900
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• 2005

We consider the second order mock theta functions defined by McIntosh and define generalized functions. We give integral representation and multibasic expansion of these functions. We also show that they are $F_q$-functions.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.97-108
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• 2014

In the theory of special functions, it is important to study some formulae describing hypergeometric functions with other hypergeometric functions. In this paper, we give some methods to obtain a lot of decomposition formulae for generalized hypergeometric functions.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.221-233
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• 2004

In this paper we introduce the concept of the McShane-Stieltjes integrals of interval-valued functions and fuzzy-number-valued functions and investigate some of their properties.