THE q-ANALOGUE OF TWISTED LERCH TYPE EULER ZETA FUNCTIONS
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q-Volkenborn integrals ([8]) and fermionic invariant q-integ-rals ([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 [수식]E;q;ε(s) = [2]q ∞Σn=0(-)nεnqsn [n]q where 0 < q < 1; R(s) > 1, ε∈ Tp, 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.
Abstract
q-Volkenborn integrals ([8]) and fermionic invariant q-integ-rals ([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 [수식]E;q;ε(s) = [2]q ∞Σn=0(-)nεnqsn [n]q where 0 < q < 1; R(s) > 1, ε∈ Tp, 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.
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