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Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($\alpha ,\beta $) | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 13، دوره 8، شماره 2، اسفند 2017، صفحه 135-144 اصل مقاله (375.35 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2017.11767.1588 | ||
| نویسندگان | ||
| Ugur Duran* ؛ Mehmet Acikgoz | ||
| Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey | ||
| تاریخ دریافت: 06 تیر 1396، تاریخ بازنگری: 22 شهریور 1396، تاریخ پذیرش: 28 شهریور 1396 | ||
| چکیده | ||
| 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. Moreover, we derive some correlations with the modified Carlitz's $q$-Bernoulli polynomials with weight ($\alpha ,\beta $), the modified degenerate Carlitz's $q$-Bernoulli polynomials with weight ($\alpha ,\beta $), the Stirling numbers of the first kind and second kind. | ||
| کلیدواژهها | ||
| Carlitz's $q$-Bernoulli polynomials؛ Stirling numbers of the first kind؛ Stirling numbers of the second kind؛ $p$-adic $q$-integral | ||
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