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

Abstract

Recently, many authors have studied twisted q-Bernoulli polynomials by using the p-adic invariant q-integral on Z p. In this paper, we define the twisted p-adic q-integral on Z p and extend our result to the twisted q-Bernoulli polynomials and numbers. Finally, we derive some various identities related to the twisted q-Bernoulli polynomials.

A note on identities of symmetry for generalized Carlitz's q-Bernoulli polynomials

“…where a ∈ Z lies in 0 ≤ a < dp N , (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]). Let UD (Z p ) be the space of uniformly differentiable functions on Z p .…”

Some new identities on the twisted carlitz's q-bernoulli numbers and q-bernstein polynomials

“…(see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]). From (4), we note that B 0,q = 0, and…”