• Honam Mathematical Journal
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• v.34 no.4
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• pp.603-614
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• 2012

Gottlieb polynomials were introduced and investigated in 1938, and then have been cited in several articles. Very recently Khan and Akhlaq introduced and investigated Gottlieb polynomials in two and three variables to give their generating functions. Subsequently, Khan and Asif investigated the generating functions for the $q$-analogue of Gottlieb polynomials. In this sequel, by modifying Khan and Akhlaq's method, Choi presented a generalization of the Gottlieb polynomials in $m$ variables to present two generating functions of the generalized Gottlieb polynomials ${\varphi}^m_n({\cdot})$. Here, we show that many formulas regarding the Gottlieb polynomials in m variables and their reducible cases can easily be obtained by using one of two generating functions for Choi's generalization of the Gottlieb polynomials in m variables expressed in terms of well-developed Lauricella series $F^{(m)}_D[{\cdot}]$.

• Honam Mathematical Journal
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• v.39 no.3
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• pp.453-463
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• 2017

The aim of this paper is to provide a class of six definite general integrals in terms of gamma function. The results are established with the help of generalized summation formulas obtained earlier by Rakha and Rathie. The results established in this paper are simple, interesting, easily established and may be useful potentially.

• Journal of the Korean Data and Information Science Society
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• v.21 no.5
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• pp.967-972
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• 2010

We shall consider estimations of an exponetiated parameter of the exponentiated Pareto distribution with known scale and threshold parameters. A quotient distribution of two independent exponentiated Pareto random variables is obtained. We also derive the distribution of the ratio of two independent exponentiated Pareto random variables.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.509-512
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• 2007

We aim at deriving Gauss's second summation theorem for the series $_2F_1(1/2)$ by using Euler's integral representation for $_2F_1$. It seems that this method of proof has not been tried.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.467-474
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• 2022

In this article, we consider the integral operator 𝓒^b,c, which is defined as follows: $${\mathcal{C}}^{b,c}(f)(z)={\displaystyle\smashmargin{2}{\int\nolimits_{0}}^z}{\frac{f(w)*F(1,1;c;w)}{w(1-w)^{b+1-c}}}dw,$$ where * denotes the Hadamard/ convolution product of power series, F(a, b; c; z) is the classical hypergeometric function with b, c > 0, b + 1 > c and f(0) = 0. We investigate the boundedness of the 𝓒^b,c operators on Bloch spaces.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.681-692
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• 2022

Special functions and Geometric function theory are close related to each other due to the surprise use of hypergeometric function in the solution of the Bieberbach conjecture. The purpose of this paper is to provide a set of sufficient conditions under which the normalized four parametric Wright function has lower bounds for the ratios to its partial sums and as well as for their derivatives. The sufficient conditions are also obtained by using Alexander transform. The results of this paper are generalized and also improved the work of M. Din et al. [15]. Some examples are also discussed for the sake of better understanding of this article.

• Honam Mathematical Journal
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• v.38 no.1
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• pp.25-37
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• 2016

In 1972, Andrews derived the basic analogue of Gauss's second summation theorem and Bailey's theorem by implementing basic analogue of Kummer's theorem into identity due to Jackson. Recently Lavoie et.al. derived many results closely related to Kummer's theorem, Gauss's second summation theorem and Bailey's theorem and also Rakha et. al. derive the basic analogues of results closely related Kummer's theorem. The aim of this paper is to derive basic analogues of results closely related Gauss's second summation theorem and Bailey's theorem. Some applications and limiting cases are also considered.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.549-560
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• 2018

Since Mittag-Leffler introduced the so-called Mittag-Leffler function in 1903, due to its usefulness and diverse applications, a variety and large number of its extensions (and generalizations) and variants have been presented and investigated. In this sequel, we aim to introduce a new extension of the Mittag-Leffler function by using a known extended beta function. Then we investigate ceratin useful properties and formulas associated with the extended Mittag-Leffler function such as integral representation, Mellin transform, recurrence relation, and derivative formulas. We also introduce an extended Riemann-Liouville fractional derivative to present a fractional derivative formula for a known extended Mittag-Leffler function, the result of which is expressed in terms of the new extended Mittag-Leffler functions.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.139-168
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• 2016

In this work, we rst introduce a class of analytic functions involving the Dziok-Srivastava linear operator that generalizes the class of uniformly starlike functions with respect to symmetric points. We then establish the closure of certain well-known integral transforms under this analytic function class. This behaviour leads to various radius results for these integral transforms. Some of the interesting consequences of these results are outlined. Further, the lower bounds for the ratio between the functions f(z) in the class under discussion, their partial sums $f_m(z)$ and the corresponding derivative functions f'(z) and $f^{\prime}_m(z)$ are determined by using the coecient estimates.