# THE q-ANALOGUE OF TWISTED LERCH TYPE EULER ZETA FUNCTIONS

• Jang, Lee-Chae
• Published : 2010.11.30
• 58 6

#### Abstract

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.

#### Keywords

p-adic q-integral;q-Euler number and polynomials;q-Euler zeta functions;Lerch type q-Euler zeta functions

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#### Cited by

1. A New Family of q-analogue of Genocchi Numbers and Polynomials of Higher Order vol.54, pp.1, 2014, https://doi.org/10.5666/KMJ.2014.54.1.131
2. A NOTE ON THE TWISTED LERCH TYPE EULER ZETA FUNCTIONS vol.50, pp.2, 2013, https://doi.org/10.4134/BKMS.2013.50.2.659
3. On the Dirichlet’s type of Eulerian polynomials vol.8, pp.2, 2014, https://doi.org/10.1007/s40096-014-0131-8

#### Acknowledgement

Supported by : Konkuk University