• Bulletin of the Korean Mathematical Society
• /
• v.51 no.2
• /
• pp.401-408
• /
• 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
• /
• v.35 no.3_4
• /
• pp.303-311
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.299-306
• /
• 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.

• Journal for History of Mathematics
• /
• v.20 no.3
• /
• pp.27-42
• /
• 2007

Many countries in the world are celebrating the tercentenary of the birth of L. Euler. One of them to notice is the construction of the Euler Archive, which is an online archive, made by two Ph.D. graduates from Dartmouth College. On the appearance of the archive, the authors remind of the life and works of mathematician L. Euler, who is considered as the most prolific, prominent, and versatile mathematician with the huge volume of his works as well as their importances, in the history of mathematics. Celebrating the 300th birthyear of L. Euler and the appearance of Euler Archive, authors suggest The Korean Society for History of Mathematics of investigating on Euler by ourselves as Koreans, and furthermore translating some works of his. Such works may stimulate interests in mathematics and its history to students as well as scholars.

• Bulletin of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1181-1188
• /
• 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
• /
• v.36 no.5_6
• /
• pp.555-565
• /
• 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
• /
• v.37 no.3_4
• /
• pp.259-270
• /
• 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
• /
• v.39 no.1_2
• /
• pp.1-11
• /
• 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
• /
• v.34 no.1_2
• /
• pp.107-114
• /
• 2016

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

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.47-61
• /
• 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.