A Study on the Fermionic -Adic -Integral Representation on Associated with Weighted -Bernstein and -Genocchi Polynomials

On the Fermionic p-adic Integral Representation of Bernstein Polynomials Associated with Euler Numbers and Polynomials

Throughout this paper, let p be an odd prime number. The symbol, p, p , and p denote the ring of p-adic integers, the field of p-adic rational numbers, the complex number field and the completion of algebraic closure of p , respectively. Let be the set of natural numbers and ∪ {0}. Let νp be the normalized exponential valuation of p with |p|p p−νp p 1/p. Note that p {x | |x|p ≤ 1} lim← N /p p. ...

A Study on the p-Adic Integral Representation on Zp Associated with Bernstein and Bernoulli Polynomials

On the p-Adic Integral Representation of Bernstein Polynomials Associated with (h, q)-Genocchi Numbers and Polynomials

Throughout this paper, let p be a fixed odd prime number. The symbol, Zp, Qp and Cp denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp. Let N be the set of natural numbers and Z+ = N ∪ {0}. As well known definition, the p-adic absolute value is given by |x|p = p−r where x = p t s with (t, p) = (s, p) = (t, s) = 1. When one talk...

A Study on the p-Adic q-Integral Representation on Zp Associated with the Weighted q-Bernstein and q-Bernoulli Polynomials

Let p be a fixed prime number. Throughout this paper, p, p , and p will denote the ring of p-adic integers, the field of p-adic rational numbers, and the completion of the algebraic closure of p , respectively. Let be the set of natural numbers, and let ∪ {0}. Let νp be the normalized exponential valuation of p with |p|p p−νp p 1/p. Let q be regarded as either a complex number q ∈ or a p-adic n...

Calculating Zeros of the q-Genocchi Polynomials Associated with p-adic q-Integral on ℤp

In this paper we construct the new analogues of Genocchi the numbers and polynomials. We also observe the behavior of complex roots of the q-Genocchi polynomials Gn,q x , using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the q-Genocchi polynomials Gn,q x . Finally, we give a table for the solutions of the q-Ge...