17 research outputs found
Interpolation function of the genocchi type polynomials
The main purpose of this paper is to construct not only generating functions
of the new approach Genocchi type numbers and polynomials but also
interpolation function of these numbers and polynomials which are related to a,
b, c arbitrary positive real parameters. We prove multiplication theorem of
these polynomials. Furthermore, we give some identities and applications
associated with these numbers, polynomials and their interpolation functions.Comment: 14 page
A note on the modified q-Dedekind sums
In the present paper, the fundamental aim is to consider a p-adic continuous
function for an odd prime to inside a p-adic q-analogue of the higher order
modified Dedekind-type sums related to q-Genocchi polynomials with weight alpha
by using fermionic p-adic invariant q-integral on Zp.Comment: 6 page
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