On the families of q-Euler numbers and polynomials and their applications

In the present paper, we investigate special generalized q-Euler numbers and polynomials. Some earlier results of T. Kim in terms of q-Euler polynomials with weight alpha can be deduced. For presentation of our formulas we apply the method of generating function and p-adic q-integral representation on Zp. We summarize our results as follows. In section 2, by using combinatorial techniques we present two formulas for q-Euler numbers with weight alpha. In section 3, we derive distribution formula (Multiplication Theorem) for Dirichlet type of q-Euler numbers and polynomials with weight . Moreover we define partial Dirichlet type zeta function and Dirichlet q-L-function, and obtain some interesting combinatorial identities for interpolating our new definitions. In addition, we derive behavior of the Dirichlet type of q-Euler L-function with weight alpha, Lq (s; x j) at s = 0. Furthermore by using second kind stirling numbers, we obtain an explicit formula for Dirichlet type q-Euler numbers with weight alpha. Moreover a novel formula for q-Euler-Zeta function with weight in terms of nested series of E;q (n j) is derived . In section 4, by introducing p-adic Dirichlet type of q-Euler measure with weight, and we obtain some combinatorial relations, which interpolate our previous results. In section 5, which is the main section of our paper. As an application, we introduce a novel concept of dynamics of the zeros of analytically continued q-Euler polynomials with weight alpha.Comment: 15 pages, submitte

On the Twisted q-Euler numbers and polynomials associated with basic q-l-functions

One purpose of this paper is to construct twisted q-Euler numbers by using p-adic invariant integral on Zp in the sense of fermionic. Finally, we consider twisted Euler q-zeta function and q-l-series which interpolate twisted q-Euler numbers and polynomials.Comment: 8 page

Quenched KS light hadron mass at \beta=6.5 on a 64\times 48^3 lattice

We report our quenched staggered light hadron mass calculation at the coupling of \beta = 6.5 on a 48^3 \times 64 lattice, based on an increased statistics of two hundred gauge configurations. Staggered quark wall sources with mass of m_q a = 0.01, 0.005, 0.0025 and 0.00125 are used. Flavor symmetry is restored for pion and \rho meson. The lattice scale is estimated to be a^{-1} = 3.7(2) GeV.Comment: 4 pages, espcrc2.sty, epsf.sty, Poster presented at LATTICE96(poster

New identities involving q-Euler polynomials of higher order

In this paper we give new identities involving q-Euler polynomials of higher order.Comment: 11 page