791 research outputs found
A note on the values of the weighted q-Bernstein polynomials and modified q-Genocchi numbers with weight alpha and beta via the p-adic q-integral on Zp
The rapid development of q-calculus has led to the discovery of new
generalizations of Bernstein polynomials and Genocchi polynomials involving
q-integers. The present paper deals with weighted q-Bernstein polynomials and
q-Genocchi numbers with weight alpha and beta. We apply the method of
generating function and p-adic q-integral representation on Zp, which are
exploited to derive further classes of Bernstein polynomials and q-Genocchi
numbers and polynomials. To be more precise we summarize our results as
follows, we obtain some combinatorial relations between q-Genocchi numbers and
polynomials with weight alpha and beta. Furthermore, we derive an integral
representation of weighted q-Bernstein polynomials of degree n on Zp. Also we
deduce a fermionic p-adic q-integral representation of product weighted
q-Bernstein polynomials of different degrees n1,n2,...on Zp and show that it
can be written with q-Genocchi numbers with weight alpha and beta which yields
a deeper insight into the effectiveness of this type of generalizations. Our
new generating function possess a number of interesting properties which we
state in this paper.Comment: 10 page
Some New Identities of Genocchi Numbers and Polynomials involving Bernoulli and Euler polynomials
In this paper, we will deal with some new formulae for two product Genocchi
polynomials together with both Euler polynomials and Bernoulli polynomials. We
get some applications for Genocchi polynomials. Our applications possess a
number of interesting properties to study in Theory of Analytic numbers which
we express in the present paper.Comment: 10 pages, submitte
The Evaluation of the Sums of More General Series by Bernstein Polynomials
Let n,k be the positive integers, and let S_{k}(n) be the sums of the k-th
power of positive integers up to n. By means of that we consider the evaluation
of the sum of more general series by Bernstein polynomials. Additionally we
show the reality of our idea with some examples.Comment: 6 pages, submitte
Analytic Continuation of weighted q-Genocchi numbers and polynomials
In the present paper, we analyse analytic continuation of weighted q-Genocchi
numbers and polynomials. A novel formula for weighted q-Genocchi- Zeta function
{\zeta}G,q (s | {\alpha}) in terms of nested series of {\zeta}G,q (n |
{\alpha}) is derived. Moreover, we introduce a novel concept of dynamics of the
zeros of analytically continued weighted q-Genocchi polynomials.Comment: 5 pages, submitte
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