• 대한수학회논문집
• /
• 제14권3호
• /
• pp.641-647
• /
• 1999

The object of this note is to give sums of certain families of series which are initiated from their special cases considered here. Pelevant connections of the series identities presented here with those given elsewhere are also pointed out.

• Korean Journal of Mathematics
• /
• 제25권1호
• /
• pp.87-97
• /
• 2017

In [9], we computed shadows of the second order mock theta functions and showed that they are essentially same with the shadow of a mock theta function related to the Mathieu moonshine phenomenon. In this paper, we further survey the second order mock theta functions on their quantum modularity and their behavior in the lower half plane.

• Kyungpook Mathematical Journal
• /
• 제45권1호
• /
• pp.1-11
• /
• 2005

Making use of the multidimensional fractional calculus operators introduced in [20], this paper gives the images under these operators of the celebrated Fox's H-function. Special cases are briefly point out, and some of the results are also studied on general spaces of functions $M_{\lambda}(R_{+}^n)$.

• Journal of the Korean Data and Information Science Society
• /
• 제21권5호
• /
• pp.967-972
• /
• 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.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제19권2호
• /
• pp.87-102
• /
• 2012

In this paper, we consider the Fourier-type functionals introduced in [16]. We then establish the analytic Feynman integral for the Fourier-type functionals. Further, we get a series expansion of the analytic Feynman integral for the Fourier-type functional $[{\Delta}^kF]^{\^}$. We conclude by applying our series expansion to several interesting functionals.

• 대한수학회지
• /
• 제54권6호
• /
• pp.1641-1665
• /
• 2017

The paper considers p-valent functions in the open unit disk. We study the integral means along with the area integral problems for functions belonging to a family of p-valent functions.

• 대한수학회논문집
• /
• 제22권4호
• /
• pp.509-512
• /
• 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.

• Kyungpook Mathematical Journal
• /
• 제51권2호
• /
• pp.217-232
• /
• 2011

Differential subordination and superordination results are obtained for multivalent meromorphic functions associated with the Liu-Srivastava linear operator in the punctured unit disk. These results are derived by investigating appropriate classes of admissible functions. Sandwich-type results are also obtained.

• East Asian mathematical journal
• /
• 제18권1호
• /
• pp.1-13
• /
• 2002

Some Miller-Mocanu type arguments are used here in order to establish a general starlikeness condition involving the familiar Ruscheweyh derivative. Relevant connections with the various known starlikeness conditions are also indicated. This paper concludes with several remarks and observations in regard especially to the nonsharpness of the main starlike condition presented here.

• Kyungpook Mathematical Journal
• /
• 제56권1호
• /
• pp.173-184
• /
• 2016

Mock theta functions are the most interesting topic mentioned in Ramanujan's Lost Notebook, due to its emerging application in the field of Number theory, Quantum invariants theory and etc. In the present research articles we have made an attempt to develop continued fractions representation of all the existing Mock theta functions.