• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.303-311
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• 2017

In this paper we define (p, q)-analogue of Euler zeta function. In order to define (p, q)-analogue of Euler zeta function, we introduce the (p, q)-analogue of Euler numbers and polynomials by generalizing the Euler numbers and polynomials, Carlitz's type q-Euler numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with (p, q)-analogue of Euler numbers and polynomials. Finally, we investigate the zeros of the (p, q)-analogue of Euler polynomials by using computer.

• 대한수학회보
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• 제51권2호
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• pp.401-408
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• 2014

We establish a new approach for the sums of products of the Euler numbers by using the relation of values at non-positive integers of the representation of the multiple Hurwitz-Euler eta function in terms of the Hurwitz-Euler eta function.

• 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 $E_{n,p,q}$.

• Journal of applied mathematics & informatics
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• 제37권3_4호
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• pp.259-270
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• 2019

In this paper we define the degenerate Carlitz-type q-Euler polynomials by generalizing the degenerate Euler numbers and polynomials, degenerate Carlitz-type Euler numbers and polynomials. We also give some interesting properties, explicit formulas, a connection with degenerate Carlitz-type q-Euler numbers and polynomials.

• Journal of applied mathematics & informatics
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• 제39권1_2호
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• pp.1-11
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• 2021

In this paper, we define degenerate Carlitz-type twisted q-Euler numbers and polynomials by generalizing the degenerate Euler numbers and polynomials, Carlitz's type degenerate q-Euler numbers and polynomials. We also give some interesting properties, explicit formulas, symmetric properties, a connection with degenerate Carlitz-type twisted q-Euler numbers and polynomials.

• Journal of applied mathematics & informatics
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• 제34권1_2호
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• pp.107-114
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• 2016

In this paper we give some symmetric property of the generalized twisted q-Euler zeta functions and q-Euler polynomials.

• 대한수학회보
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• 제41권2호
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• pp.299-306
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• 2004

In this paper, we shall construct generating function of twisted generalized Euler numbers. By using this function, we shall define twisted generalized Euler polynomials and numbers. We shall give some basic properties of these polynomials and numbers.

• 대한수학회보
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• 제47권6호
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• pp.1181-1188
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• 2010

q-Volkenborn integrals ([8]) and fermionic invariant q-integrals ([12]) are introduced by T. Kim. By using these integrals, Euler q-zeta functions are introduced by T. Kim ([18]). Then, by using the Euler q-zeta functions, S.-H. Rim, S. J. Lee, E. J. Moon, and J. H. Jin ([25]) studied q-Genocchi zeta functions. And also Y. H. Kim, W. Kim, and C. S. Ryoo ([7]) investigated twisted q-zeta functions and their applications. In this paper, we consider the q-analogue of twisted Lerch type Euler zeta functions defined by $${\varsigma}E,q,\varepsilon(s)=[2]q \sum\limits_{n=0}^\infty\frac{(-1)^n\epsilon^nq^{sn}}{[n]_q}$$ where 0 < q < 1, $\mathfrak{R}$(s) > 1, $\varepsilon{\in}T_p$, which are compared with Euler q-zeta functions in the reference ([18]). Furthermore, we give the q-extensions of the above twisted Lerch type Euler zeta functions at negative integers which interpolate twisted q-Euler polynomials.

• 한국수학사학회지
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• 제20권3호
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• pp.27-42
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• 2007

오일러의 탄생 300주년을 기념하여 2007년에 세계 각국에서는 각종 학술행사가 계획되고, 미국에는 오일러의 업적을 온라인상에 모아놓은 Euler Archive가 생겼다. 본 글에서는 Euler Archive의 활용을 제안하는 한편, 현재에 이르기까지 수학사상 가장 많은 업적을 일궈낸 오일러의 삶을 간단히 돌아보고, 그가 증명한 수학 정리들 중에서 가장 대표적인 10개의 정리들에 대한 배경과 수학 지식세계에 미친 영향을 살펴봄으로써 오일러의 탄생 300주년을 축하하고자 한다.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.873-882
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• 2022

In this paper, we construct the multiple (h, p, q)-Hurwitz-Euler eta function by generalizing the multiple Hurwitz-Euler eta function. We get some explicit formulas and properties of the higher-order (h, p, q)-Euler numbers and polynomials.