Calculating Zeros of the -Genocchi Polynomials Associated with -Adic -Integral on

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...

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...

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. ...

Integral Formulae of Bernoulli and Genocchi Polynomials

On Integral Zeros of Krawtchouk Polynomials

We derive new conditions for nonexistence of integral zeros of binary Krawtchouk polynomials. Upper bounds for the number of integral roots of Krawtchouk polynomials are presented.