New q-Euler numbers and polynomials associated with p-adic q-integrals

In this paper we study q-Euler numbers and polynomials by using p-adic q-fermionic integrals on Z_p. The methods to study q-Euler numbers and polynomials in this paper are new.Comment: 13 page

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 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

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

Shape invariance approach to exact solutions of the Klein-Gordon equation

Using the shape invariance property we obtain exact solutions of the (1+1)dimensional Klein-Gordon equation for certain types of scalar and vector potentials. We also discuss the possibility of obtaining real energy spectrum with non-Hermitian interaction within this framework

A note on q-Euler numbers and polynomials

The purpose of this paper is to construct q-Euler numbers and polynomials by using p-adic q-integral equations on Zp. Finally, we will give some interesting formulae related to these q-Euler numbers and polynomials.Comment: 6 page