• Kyungpook Mathematical Journal
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• 제22권1호
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• pp.21-27
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• 1982

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1289-1295
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• 2008

We find the generalized characteristic polynomial of graphs G($F_{1},F_{2},{\cdots},F_{v}$) the semi-zigzag product of G and ${\{F_{i}\}^{v}_{i=1}$ obtained from G by replacing vertices by circulant graphs of vertices and joining $F_{i}$'s along the edges of G. These graphs contain discrete tori and are key examples in the study of network model.

• 호남수학학술지
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• 제42권2호
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• pp.251-268
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• 2020

In this paper, we estimate the degree of approximation by means of the complete modulus of continuity, the partial modulus of continuity, the Lipschitz-type class and Petree's K-functional for the bivariate Szász-Kantorovich operators based on Brenke-type polynomials. Later, we construct Generalized Boolean Sum operators associated with combinations of the Szász-Kantorovich operators based on Brenke-type polynomials. In addition, we obtain the rate of convergence for the GBS operators with the help of the mixed modulus of continuity and the Lipschitz class of the Bögel continuous functions.

• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.307-313
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• 2006

In this paper, we first establish an interesting new finite integral whose integrand involves the product of a general class of polynomials introduced by Srivastava [13] and the generalized H-function ([9], [10]) having general argument. Next, we present five special cases of our main integral which are also quite general in nature and of interest by themselves. The first three integrals involve the product of $\bar{H}$-function with Jacobi polynomial, the product of two Jacobi polynomials and the product of two general binomial factors respectively. The fourth integral involves product of Jacobi polynomial and well known Fox's H-function and the last integral involves product of a Jacobi polynomial and 'g' function connected with a certain class of Feynman integral which may have practical applications.

• Kyungpook Mathematical Journal
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• 제54권4호
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• pp.639-653
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• 2014

In [9], Kauffman introduced virtual knot theory and generalized many classical knot invariants to virtual ones. For example, he extended the Jones polynomials $V_K(t)$ of classical links to the f-polynomials $f_K(A)$ of virtual links by using bracket polynomials. In [4], M. Goussarov, M. Polyak and O. Viro introduced finite type invariants of virtual knots. In this paper, we give a necessary condition for a virtual knot invariant to be of finite type by using $t(a_1,{\cdots},a_m)$-sequences of virtual knots. Then we show that the higher derivatives $f_K^{(n)}(a)$ of the f-polynomial $f_K(A)$ of a virtual knot K at any point a are not of finite type unless $n{\leq}1$ and a = 1.

• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.725-734
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• 2019

The aim of this paper is to establish two general finite integral formulas involving the product of Galué type Struve functions and Srivastava's polynomials. The results are given in terms of generalized (Wright's) hypergeometric functions. These results are obtained with the help of finite integrals due to Oberhettinger and Lavoie-Trottier. Some interesting special cases of the main results are also considered. The results presented here are of general character and easily reducible to new and known integral formulae.

• 대한수학회논문집
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• 제33권2호
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• pp.473-484
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• 2018

In this paper, we discuss how the operational calculus can be exploited to the theory of generalized special functions of many variables and many indices. We obtained the generating relations for 3-index, 3-variable and 1-parameter Hermite polynomials. Some mixed type generating relations and bilateral generating relations of many indices and many variable like Lagurre-Hermite and Hermite-Sister Celine's polynomials are also obtained. Further we generalize some results on old symbolic notations using operational identities.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.591-600
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• 2020

This work is a continuation of our investigations for p-adic analogue of the alternating form Dirichlet L-functions $$L_E(s,{\chi})={\sum\limits_{n=1}^{\infty}}{\frac{(-1)^n{\chi}(n)}{n^s}},\;Re(s)>0$$. Let L_p,E(s, t; χ) be the p-adic Euler L-function of two variables. In this paper, for any α ∈ ℂ_p, |α|_p ≤ 1, we give a power series expansion of L_p,E(s, t; χ) in terms of the variable t. From this, we derive a power series expansion of the generalized Euler polynomials with negative index, that is, we prove that $$E_{-n,{\chi}}(t)={\sum\limits_{m=0}^{\infty}}\(\array{-n\\m}\)E_{-(m+n),{\chi}^{t^m}},\;n{\in}{\mathbb{N}}$$, where t ∈ ℂ_p with |t|_p < 1. Some further properties for L_p,E(s, t; χ) has also been shown.

• Kyungpook Mathematical Journal
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• 제11권1호
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• pp.93-99
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• 1971

In this paper, the author has established the formulae for product of two generalized hypergeometric polynomials by defining the polynomial in the form $$F_n(x)=x^{({\delta}-1)n}{_{p+{\delta}}F_q}\[\array{{\Delta}({\delta},-n),&a_1,&{\cdots}{\cdots},&a_p\\&b_1,&{\cdots}{\cdots},&b_q};\;{\lambda}x^c\]$$, where the symbol ${\Delta}({\delta},-n)$ represents the set of ${\delta}$-parameters: $${\frac{-n}{\delta}},\;{\frac{-n+1}{\delta}},\;{\cdots}{\cdots},\;{\frac{-n+{\delta}-1}{\delta}}$$ and ${\delta}$, n are positive integers. A number of known as well as new results have been also obtained with proper choice of parameters.

• 대한수학회보
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• 제44권1호
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• pp.1-12
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• 2007

In this paper, we consider the q-Volkenborn integral of uniformly differentiable functions on the p-adic integer ring. By using this integral, we obtain the generating functions of twisted q-generalized Bernoulli numbers and polynomials. We find some properties of these numbers and polynomials.