• Kyungpook Mathematical Journal
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• 제59권3호
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• pp.433-443
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• 2019

In this work, we evaluate the Mellin transform of the Marichev-Saigo-Maeda fractional integral operator with Appell's function $F_3$ type kernel. We then discuss six special cases of the result involving the Saigo fractional integral operator, the $Erd{\acute{e}}lyi$-Kober fractional integral operator, the Riemann-Liouville fractional integral operator and the Weyl fractional integral operator. We obtain new and known results as special cases of our main results. Finally, we obtain the images of S-generalized Gauss hypergeometric function under the operators of our study.

• 호남수학학술지
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• 제39권4호
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• pp.561-568
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• 2017

Hurwitz zeta function occurs in various parts of mathematics. In particular, it plays an important role in some area of number theory. In this paper, using a certain transformation formula, we find some identities of relations between ${\zeta}(2n+1)$ and ${\zeta}(2n+1,{\alpha})$ for special values of ${\alpha}$.

• 대한수학회보
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• 제55권1호
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• pp.51-61
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• 2018

In this article, we mainly use Nevanlinna theory to investigate some special difference equations of malmquist type such as $f^2+({\Delta}_cf)^2={\beta}^2$, $f^2+({\Delta}_cf)^2=R$, $f{^{\prime}^2}+({\Delta}_cf)^2=R$ and $f^2+(f(z+c))^2=R$, where ${\beta}$ is a nonzero small function of f and R is a nonzero rational function respectively. These discussions extend one related result due to C. C. Yang et al. in some sense

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 봄 학술발표회 논문집
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• pp.110-118
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• 2001

In many areas of finite element analysis, elements with special properties are required to achieve maximal accuracy. As examples, we may mention infinite elements for the representation of spatial domain that extend to special and singular elements for modeling point and line singularities engendered by geomeric features such as reentrant corners and cracks. In this paper, we study on modified shape function representing singular properties and algorigthm for the pollution adaptive mesh generation. We will also show that the modified shape function reduces pollution error and local error.

• Kyungpook Mathematical Journal
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• 제58권4호
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• pp.615-625
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• 2018

In this paper, we discuss the connection between the 5-dimensional complex Lie algebra ${\mathcal{K}} _5$ and Special functions. We construct certain two variable models of the irreducible representations of ${\mathcal{K}}_5$. We also use an Euler type integral transformation to obtain the new transformed models, in which the basis function appears as $_2F_1$. Further, we utilize these models to get some generating functions and recurrence relations.

• 대한수학회논문집
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• 제36권4호
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• pp.705-714
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• 2021

The Whittaker function and its diverse extensions have been actively investigated. Here we aim to introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function 𝚽_p,v and investigate some of its formulas such as integral representations, a transformation formula, Mellin transform, and a differential formula. Some special cases of our results are also considered.

• Kyungpook Mathematical Journal
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• 제61권4호
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• pp.765-779
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• 2021

The fundamental goal of this paper is to investigate some inequalities involving the special beta function in n variables. Our theoretical results obtained here are extensions and refinements for some inequalities already discussed in the literature.

• Kyungpook Mathematical Journal
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• 제50권2호
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• pp.177-193
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• 2010

Working with the various special functions of mathematical physics and applied mathematics we often encounter inverse relations of the type $F_n(x)=\sum\limits_{k=0}^{n}A^n_kG_k(x)$ and $ G_n(x)=\sum\limits_{k=0}^{n}B_k^nF_k(x)$, where 0, 1, 2,$\cdots$. Here $F_n(x)$, $G_n(x)$ denote special polynomial functions, and $A_k^n$, $B_k^n$ denote coefficients found by use of the orthogonal properties of $F_n(x)$ and $G_n(x)$, or by skillful series manipulations. Typically $G_n(x)=x^n$ and $F_n(x)=P_n(x)$, the n-th Legendre polynomial. We give a collection of inverse series pairs of the type $f(n)=\sum\limits_{k=0}^{n}A_k^ng(k)$ if and only if $g(n)=\sum\limits_{k=0}^{n}B_k^nf(k)$, each pair being based on some reasonably well-known special function. We also state and prove an interesting generalization of a theorem of Rainville in this form.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.83-99
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• 2002

Optimality conditions are derived for a nonlinear program in which a support function appears in the objective as well as in each constraint function. Wolfe and Mond-Weir type duals to this program are presented and various duality results are established under suitable convexity and generalized convexity assumptions. Special cases that often occur in the literature are those in which a support function is the square root of a positive semi- definite quadratic form or an Lp norm. It is pointed out that these special cases can easily be generated from our results.

• 대한수학회논문집
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• 제31권3호
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• pp.591-601
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• 2016

Integral transforms and fractional integral formulas involving well-known special functions are interesting in themselves and play important roles in their diverse applications. A large number of integral transforms and fractional integral formulas have been established by many authors. In this paper, we aim at establishing some (presumably) new integral transforms and fractional integral formulas for the generalized hypergeometric type function which has recently been introduced by Luo et al. [9]. Some interesting special cases of our main results are also considered.