SYMMETRIC IDENTITIES FOR TWISTED q-EULER ZETA FUNCTIONS

Abstract

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

SYMMETRIC PROPERTIES FOR GENERALIZED TWISTED q-EULER ZETA FUNCTIONS AND q-EULER POLYNOMIALS

“…In this paper, we establish some interesting symmetric identities for generalized twisted q-Euler zeta functions and generalized ] twisted q-Euler polynomials in complex field. If we take χ = 1 in all equations of this article, then [1] are the special case of our results. Throughout this paper we use the following notations.…”

“…The Euler numbers and polynomials possess many interesting properties in many areas of mathematics and physics. Many mathematicians have studied in the area of various q-extensions of Euler polynomials and numbers (see [1][2][3][4][5][6][7][8][9][10][11]). Recently, Y. Hu investigated several identities of symmetry for Carlitz's q-Bernoulli numbers and polynomials in complex field (see [3]).…”

“…Ryoo studied some identities of symmetry for q-Genocchi polynomials (see [2]). In [1], we obtained some identities of symmetry for Carlitz's twisted q-Euler zeta function in complex field. In this paper, we establish some interesting symmetric identities for generalized twisted q-Euler zeta functions and generalized ] twisted q-Euler polynomials in complex field.…”

“…By N we denote the set of natural numbers, Z denotes the ring of rational integers, Q denotes the field of rational numbers, C denotes the set of complex numbers, and Z + = N ∪ {0}. We use the following notation: [1,2,3,4]).…”

Symmetric identities for Carlitz's generalized twisted q-Bernoulli numbers and polynomials associated with p-adic q-integral on Zp

“…Many mathematicians have studies different kinds of the Euler, Bernoulli, Genocchi, Tangent numbers and polynomials(see [1][2][3][4][5][6][7][8][9][10][11]). These numbers and polynomials play important roles in many different areas of mathematics such as number theory, combinatorics, special function and analysis.…”