• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.337-346
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• 2012

In this paper we construct a new type of twisted $q$-Genocchi numbers $G_{n,q,w}^{({\alpha})}$ and polynomials $G_{n,q,w}^{({\alpha})}(x)$. Some interesting results and relationships are obtained.

• 충청수학회지
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• 제26권3호
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• pp.591-599
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• 2013

A large number of sequences of polynomials and numbers have arisen in mathematics. Some of them, for example, Bernoulli polynomials and numbers, have been investigated deeply and widely. Here we aim at presenting certain interesting and (potentially) useful identities involving mainly in the second-order Eulerian numbers and Stirling polynomials, which seem to have not been given so much attention.

• Journal of applied mathematics & informatics
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• 제36권5_6호
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• pp.555-565
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• 2018

The main subject of this paper is to introduce the (p, q)-Euler polynomials and obtain several interesting symmetric properties of the modified (p, q)-Hurwitz Euler Zeta function with regard to (p, q) Euler polynomials. In order to get symmetric properties, we introduce the new (p, q)-analogue of Euler polynomials $E_{n,p,q}(x)$ and numbers $E_{n,p,q}$.

• 대한수학회지
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• 제36권3호
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• pp.489-507
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• 1999

We investigate the asymptotic behavior of the extreme zeros of orthogonal polynomials with respect to a positive measure d$\alpha$(x) in terms of the three term recurrence coefficients. We then show that the asymptotic behavior of extreme zeros of orthogonal polynomials with respect to g(x)d$\alpha$(x) is the same as that of extreme zeros of orthogonal polynomials with respect to d$\alpha$(x) when g(x) is a polynomial with all zeros in a certain interval determined by d$\alpha$(x). several illustrating examples are also given.

• Kyungpook Mathematical Journal
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• 제54권3호
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• pp.463-469
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• 2014

In this paper, we construct new q-extension of Euler polynomials with weight 0. These modified q-Euler polynomials are useful to study various identities of Carlitz's q-Bernoulli numbers.

• 호남수학학술지
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• 제42권3호
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• pp.425-447
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• 2020

The family of q-Konhauser matrix polynomials have been extended to Konhauser matrix polynomials. The purpose of the present work is to show that an extension of the explicit forms, generating matrix functions, matrix recurrence relations and Rodrigues-type formula for these matrix polynomials are given, our desired results have been established and their applications are presented.

• 호남수학학술지
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• 제33권3호
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• pp.431-439
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• 2011

We prove two identities for multivariate Bernstein polynomials on simplex, which are considered on a pointwise. In this paper, we study good approximations of Bernstein polynomials for every continuous functions on simplex and the higher dimensional q-analogues of Bernstein polynomials on simplex.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.205-214
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• 2007

Over the years, there has been increasing interest in solving mathematical problems with the aid of computers. The main purpose of this paper is to investigate the roots of the q-Bernoulli polynomials $B_{n,q}{^r}(x)$ for values of the index n by using computer. Finally, we consider the reflection symmetries of the q-Bernoulli polynomials $B_{n,q}{^r}(x)$.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제20권4호
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• pp.595-602
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• 2006

In this paper we study an application of elementary symmetric polynomials related to transformation of homogeneous symmetric polynomials, factorization of polynomials, solving equation using elementary symmetric polynomials at the level of school mathematics.

• 대한수학회보
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• 제53권2호
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• pp.569-579
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• 2016

L. Carlitz introduced higher order degenerate Euler polynomials in [4, 5] and studied a degenerate Staudt-Clausen theorem in [4]. D. S. Kim and T. Kim gave some formulas and identities of degenerate Euler polynomials which are derived from the fermionic p-adic integrals on ${\mathbb{Z}}_p$ (see [9]). In this paper, we introduce higher order degenerate Genocchi polynomials. And we give some formulas and identities of degenerate Genocchi polynomials which are derived from the fermionic p-adic integrals on ${\mathbb{Z}}_p$.