A Note on q-analogue of Degenerate Catalan Numbers Associated with p-adic Integral on Zp

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|...

On Carlitz’s Type q-Euler Numbers Associated with the Fermionic P-Adic Integral on Zp

We consider the following problem in the paper of Kim et al. 2010 : “Find Witt’s formula for Carlitz’s type q-Euler numbers.” We give Witt’s formula for Carlitz’s type q-Euler numbers, which is an answer to the above problem. Moreover, we obtain a new p-adic q-l-function lp,q s, χ for Dirichlet’s character χ, with the property that lp,q −n, χ En,χn,q − χn p p nqEn,χn,qp for n 0, 1, . . . using ...

Notes on Degenerate Twisted (h, q)-Tangent Numbers and Polynomials Associated with the p-Adic Integral on Zp

A Note on the Twisted (h, q)-Tangent Numbers and Polynomials Associated with the p-Adic Integral on Zp

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper we introduce the twisted (h, q)-tangent numbers T (h) n,q,w and polynomials T (h) n,q,w (x). Some interesting results and relationships are obtained.

A NOTE ON p-ADIC q-INTEGRAL ASSOCIATED WITH q-EULER NUMBERS

Abstract. We show that q-Euler numbers can be represented as an integral by the q-analogue of the ordinary p-adic fermionic measure, whence we give an answer to the question of readers to ask us for the fermionic p-adic q-integral on Zp. Sometimes several readers give the nonsense comments to us. But we do not write their names in this paper. I would like to tell the readers that papers are dif...