q-Bernoulli numbers and q-Bernoulli polynomials revisited
نویسندگان
چکیده
منابع مشابه
On the weighted degenerate Carlitz q-Bernoulli polynomials and numbers
In this paper, by using the p-adic q-integral on Zp which was defined by Kim, we define the weighted Carlitz q-Bernoulli polynomials and investigate some identities of these polynomials. In particular, we define the weighted degenerate Carlitz’s q-Bernoulli polynomials and numbers and give some interesting properties that are associated with these numbers and polynomials. AMS subject classifica...
متن کاملA note on q-Bernoulli numbers and polynomials
By using q-integration, we will give some integral equation which are related to the Barnes’ multiple Bernoulli numbers. The object of this paper is to give explicit q-integral’s formulae which are related to Barnes’ multiple q-Bernoulli polynomials. §
متن کاملA note on q-Bernoulli numbers and polynomials
Abstract Recently, B. A. Kupershmidt have constructed a reflection symmetries of q-Bernoulli polynomials (see [9]). In this paper we give another construction of a q-Bernoulli polynomials, which form Barnes’ multiple Bernoulli polynomials at q = 1, cf. [1, 13, 14]. By using q-Volkenborn integration, we can also investigate the properties of the reflection symmetries of these’ q-Bernoulli polyno...
متن کاملq-BERNOULLI NUMBERS AND POLYNOMIALS ASSOCIATED WITH GAUSSIAN BINOMIAL COEFFICIENT
Let q be regarded as either a complex number q ∈ C or a p-adic number q ∈ Cp. If q ∈ C, then we always assume |q| < 1. If q ∈ Cp, we normally assume |1− q|p < p − 1 p−1 , which implies that q = exp(x log q) for |x|p ≤ 1. Here, | · |p is the p-adic absolute value in Cp with |p|p = 1 p . The q-basic natural number are defined by [n]q = 1−q 1−q = 1 + q + · · · + q , ( n ∈ N), and q-factorial are a...
متن کاملModified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($alpha ,beta $)
The main goal of the present paper is to construct some families of the Carlitz's $q$-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's $q$-Bernoulli polynomials and numbers with weight ($_{p}$. We then define the modified degenerate Carlitz's $q$-Bernoulli polynomials and numbers with weight ($alpha ,beta $) and obtain some recurrence relations and other identities...
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2011
ISSN: 1687-1847
DOI: 10.1186/1687-1847-2011-33