• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.465-474
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• 2014

Many mathematicians have studied various relations beween Euler number $E_n$, Bernoulli number $B_n$ and Genocchi number $G_n$ (see [1-18]). They have found numerous important applications in number theory. Howard, T.Agoh, S.-H.Rim have studied Genocchi numbers, Bernoulli numbers, Euler numbers and polynomials of these numbers [1,5,9,15]. T.Kim, M.Cenkci, C.S.Ryoo, L. Jang have studied the q-extension of Euler and Genocchi numbers and polynomials [6,8,10,11,14,17]. In this paper, our aim is introducing and investigating an extension term of generalized Euler polynomials. We also obtain some identities and relations involving the Euler numbers and the Euler polynomials, the Genocchi numbers and Genocchi polynomials.

• 충청수학회지
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• 제29권2호
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• pp.283-286
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• 2016

In this paper, we find a new recurrence formula of the Euler zeta functions.

• 대한수학회보
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• 제36권1호
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• pp.47-61
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• 1999

In this paper we difine poly-Euler numbers which generalize ordinary Euler numbers. We construct a p-adic poly-Euler measure by the poly-Euler polynomials and derive an integral formula.

• Journal of applied mathematics & informatics
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• 제36권5_6호
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• pp.369-379
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• 2018

We consider a p-adic Euler L-function of two variables which interpolate the generalized Euler polynomials at nonpositive integers. We also show that the reflection formula and the functional equation for these functions.

• 한국항공우주학회지
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• 제36권2호
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• pp.115-122
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• 2008

예조건화 오일러 방정식의 수렴 특성에 미치는 특성 조건수의 영향을 조사하였다. 그리고 Choi와 Merkle 예조건화를 적용한 경우와 온도 예조건화를 적용한 경우의 수렴 특성을 분석하였다. 공간차분을 위해 예조건화 Roe의 FDS 기법을 적용하였고, 시간적분을 위해 예조건화 LU-SGS 기법을 적용하였다. 지배방정식의 수렴 특성은 특성 조건수에 크게 영향을 받는 것으로 나타났으며, 최적의 특성 조건수가 존재하는 것으로 나타났다. 그리고 최적의 특성 조건수는 Choi 와 Merkle 예조건화를 적용한 경우와 온도 예조건화를 적용한 경우가 서로 다른 것으로 나타났다.

• 대한수학회보
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• 제50권2호
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• pp.659-665
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• 2013

In this note, the $q$-extension of the twisted Lerch Euler zeta functions considered by Jang [Bull. Korean Math. Soc. 47 (2010), no. 6, 1181-1188] is further investigated, and the generalized multiplication theorem for the $q$-extension of the twisted Lerch Euler zeta functions is given. As applications, some well-known results in the references are deduced as special cases.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.133-159
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• 2024

In a previous work we studied generalized Stirling numbers of the second kind S^{(a₂,b₂,p₂)}_a1,b1 (p₁, k), where a₁, a₂, b₁, b₂ are given complex numbers, a₁, a₂ ≠ 0, and p₁, p₂ are non-negative integers given. In this work we use these generalized Stirling numbers to define Bernoulli polynomials in two variables B_p1,p2 (x₁, x₂), and Euler polynomials in two variables E_p1p2 (x₁, x₂). By using results for S^{(1,x₂,p₂)}_1,x1 (p₁, k), we obtain generalizations, to the bivariate case, of some well-known properties from the standard case, as addition formulas, difference equations and sums of powers. We obtain some identities for bivariate Bernoulli and Euler polynomials, and some generalizations, to the bivariate case, of several known identities for Bernoulli and Euler numbers and polynomials of the standard case.

• 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.

• Journal of applied mathematics & informatics
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• 제35권5_6호
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• pp.599-609
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• 2017

We construct degenerated Euler polynomials of the second kind and find some basic properties of this polynomials. From this paper, we can see degenerated alternative power sum is defined and is related to degenerated Euler polynomials of the second kind. Using this power sum, we have a number of symmetric properties of degenerated Euler polynomials of the second kind.

• 대한수학회논문집
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• 제36권1호
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• pp.19-26
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• 2021

Degenerate versions of the special polynomials and numbers since they have many applications in analytic number theory, combinatorial analysis and p-adic analysis. In this paper, we define the degenerate poly-Euler numbers and polynomials arising from the modified polyexponential functions. We derive explicit relations for these numbers and polynomials. Also, we obtain some identities involving these polynomials and some other special numbers and polynomials.