A Note on the -Euler Numbers and Polynomials with Weak Weight

We construct a new type of -Euler numbers and polynomials with weak weight : (),, (),(), respectively. Some interesting results and relationships are obtained. Also, we observe the behavior of roots of the -Euler numbers (), and polynomials (),() with weak weight . By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of -Euler polynomials (), with weak weight

A Note on the Symmetric Properties for the q-Twisted Tangent Polynomials

Abstract In [4], we studied the twisted q-tangent numbers and polynomials. By using these numbers and polynomials, we give some interesting relations between the power sums and the the twisted Tangent polynomials

Dynamics of the Zeros of Analytic Continued (

In this paper, we study that the (h,q)-Euler numbers En,q(h) and (h,q)-Euler polynomials En,q(h)(x) are analytic continued to Eq(h)(s) and Eq(h)(s,w). We investigate the new concept of dynamics of the zeros of analytic continued polynomials related to solution of Bernoulli equation. Finally, we observe an interesting phenomenon of “scattering” of the zeros of Eq(h)(s,w)

A note on q-Bernoulli numbers and polynomials

By using p-adic q-integrals, we study the q-Bernoulli numbers and polynomials of higher order.Comment: 8 page

A Note on the Generalized -Bernoulli Measures with Weight

We discuss a new concept of the -extension of Bernoulli measure. From those measures, we derive some interesting properties on the generalized -Bernoulli numbers with weight attached to

Some Identities between the Extended -Bernstein Polynomials with Weight and -Bernoulli Polynomials with Weight (,)

Using bosonic -adic -integral on , we give some interesting relationships between -Bernoulli numbers with weight (,) and -Bernstein polynomials with weight . Also, using -Bernstein polynomials with two variables, we derive some interesting properties associated with -Bernoulli numbers with weight (,)