(ρ, q)-Volkenborn integration

被引：12

作者：

Araci, Serkan ^{[1
]}

Duran, Ugur ^{[2
]}

Acikgoz, Mehmet ^{[2
]}

机构：

[1] Hasan Kalyoncu Univ, Fac Econ Adm & Social Sci, Dept Econ, TR-27410 Gaziantep, Turkey

[2] Gaziantep Univ, Fac Arts & Sci, Dept Math, TR-27310 Gaziantep, Turkey

来源：

JOURNAL OF NUMBER THEORY | 2017年 / 171卷

关键词：

q-Volkenborn integral; Carlitz's q-Bernoulli polynomials; (rho; q)-calculus; p-adic number; 2-PARAMETER QUANTUM ALGEBRAS; Q-EXTENSIONS; BERNOULLI; POLYNOMIALS; EULER;

D O I：

10.1016/j.jnt.2016.07.019

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the paper, we introduce an analogue of Haar distribution based on (rho, q)-numbers, as follows: mu(rho,q) (a + p(N)Z(p)) = rho(pN)/[p(N)](rho,q) (q/rho)(a) By means of this distribution, we derive (rho, q)-analogue of Volkenborn integration which is a new generalization of Kim's q-Volkenborn integration defined in [11]. From this definition, we investigate some properties of Volkenborn integration based on (rho, q)-numbers. Finally, we construct (rho, q)-Bernoulli numbers and polynomials derived from (rho, q)-Volkenborn integral and obtain some their properties. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：18 / 30

页数：13

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