@article {
author = {Duran, Ugur and Acikgoz, Mehmet},
title = {Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($\alpha ,\beta $)},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {8},
number = {2},
pages = {135-144},
year = {2017},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {10.22075/ijnaa.2017.11767.1588},
abstract = {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.},
keywords = {Carlitz's $q$-Bernoulli polynomials,Stirling numbers of the first kind,Stirling numbers of the second kind,$p$-adic $q$-integral},
url = {https://ijnaa.semnan.ac.ir/article_2791.html},
eprint = {https://ijnaa.semnan.ac.ir/article_2791_48a0eba5d8560ea93b810f1b3562b4eb.pdf}
}