p-Adic invariant integral on Zp associated with the Changhee's q-Bernoulli polynomials

p-Adic Invariant Integral on Zp Associated with the Changhee’s q-Bernoulli Polynomials

and reproduction in any medium, provided the original work is properly cited. Abstract. In this paper, we study some properties of Changhee's q-Bernou lli polynomials which are derived from p-adic invariant integral on Z p. By using these properties, we give some interesting identities related to higher-order q-Bernoulli polynomials.

Multivariate Twisted p-Adic q-Integral on Zp Associated with Twisted q-Bernoulli Polynomials and Numbers

Let p be a fixed prime number. Throughout this paper, the symbols Z,Zp,Qp,C, and Cp will denote the ring of rational integers, the ring of p-adic integers, the field of p-adic rational numbers, the complex number field, and the completion of the algebraic closure of Qp, respectively. Let N be the set of natural numbers and Z N ∪ {0}. Let vp be the normalized exponential valuation of Cp with |p|...

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

Some Properties and Identities of Bernoulli and Euler Polynomials Associated with p-adic Integral on Zp

and Applied Analysis 3 2. Some Identities of Bernoulli and Euler Polynomials By 1.4 , we get Ek ( x y ) k ∑ j 0 ( k j ) yk−jEj x , for ∈ Z . 2.1 From 2.1 , we note that Ek ( x y ) k ∑ j 0 ( k j ) yk−jEj x y k ∑ j 1 k j ( k − 1 j − 1 ) yk−jEj x . 2.2 Thus, we have k−1 ∑ j 0 ( k − 1 j ) yk−1−j Ej 1 x j 1 Ek ( x y ) − y k . 2.3 Replacing k by k 1 in 2.3 , we obtain the following proposition. Propo...

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...