منابع مشابه
q-VOLKENBORN INTEGRATION AND ITS APPLICATIONS
The main purpose of this paper is to present a systemic study of some families of multiple q-Euler numbers and polynomials. In particular, by using the q-Volkenborn integration on Zp, we construct p-adic q-Euler numbers and polynomials of higher order. We also define new generating functions of multiple q-Euler numbers and polynomials. Furthermore, we construct Euler q-Zeta function.
متن کاملA NOTE ON q-VOLKENBORN INTEGRATION
In this paper, we construct q-numbers and polynomials by using the qVolkenborn integrals.
متن کاملOn a Multidimensional Volkenborn Integral and Higher Order Bernoulli Numbers
In particular, the values at x = 0 are called Bernoulli numbers of order k, that is, Bn (0) = Bn k) (see [1, 2, 4, 5, 9, 10, 14]). When k = 1, the polynomials or numbers are called ordinary. The polynomials Bn (x) and numbers Bn were first defined and studied by Norlund [9]. Also Carlitz [2] and others investigated their properties. Recently they have been studied by Adelberg [1], Howard [5], a...
متن کاملp-ADIC DEDEKIND AND HARDY-BERNDT TYPE SUMS RELATED TO VOLKENBORN INTEGRAL ON Zp
where ((x)) = x − [x]G − 1 2 , if x / ∈ Z, ((x)) = 0, x ∈ Z, where [x]G is the largest integer ≤ x cf. ([1], [5], [9], [11], [12], [13]). In this paper, Zp, Qp, Cp, C and Z, respectively, denote the ring of p-adic integers, the field of p-adic rational numbers, the p-adic completion of the algebraic closure of Qp normalized by |p|p = p −1, and the complex field and integer numbers. Let q be an ...
متن کاملSome Identities on the Generalized q-Bernoulli Numbers and Polynomials Associated with q-Volkenborn Integrals
Let p be a fixed prime number. Throughout this paper, Zp, Qp, C, and Cp will, respectively, denote the ring of p-adic rational integer, the field of p-adic rational numbers, the complex number field, and the completion of algebraic closure of Qp. Let N be the set of natural numbers and Z {0} ∪ N. Let νp be the normalized exponential valuation of Cp with |p|p p−νp p p−1. When one talks of q-exte...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2017
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2016.07.019