(ρ,q)-Volkenborn integration

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• 作者：Serkan Araci^a ; ^{mtsrkn@hotmail.com" class="auth_mail" title="E-mail the corresponding author} ; Ugur Duran^b ; ^{duran.ugur@yahoo.com" class="auth_mail" title="E-mail the corresponding author} ; Mehmet Acikgoz^b ; ^{acikgoz@gantep.edu.tr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05A30 ; 11B65 ; 11B68 ; 11S23
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：171
• 期：Complete
• 页码：18-30
• 全文大小：311 K

文摘

In the paper, we introduce an analogue of Haar distribution based on (ρ,q)$(\rho ,q)$-numbers, as follows: By means of this distribution, we derive (ρ,q)$(\rho ,q)$-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 (ρ,q)$(\rho ,q)$-numbers. Finally, we construct (ρ,q)$(\rho ,q)$-Bernoulli numbers and polynomials derived from (ρ,q)$(\rho ,q)$-Volkenborn integral and obtain some their properties.