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http://dx.doi.org/10.4134/BKMS.2010.47.6.1181

THE q-ANALOGUE OF TWISTED LERCH TYPE EULER ZETA FUNCTIONS  

Jang, Lee-Chae (DEPARTMENTS OF MATHEMATICS AND COMPUTER SCIENCE KONKUK UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.6, 2010 , pp. 1181-1188 More about this Journal
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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Times Cited By KSCI : 2  (Citation Analysis)
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