Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($alpha ,beta $)
نویسندگان
چکیده مقاله:
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.
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عنوان ژورنال
دوره 8 شماره 2
صفحات 135- 144
تاریخ انتشار 2017-12-01
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