TY - JOUR
ID - 2791
TI - Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($\alpha ,\beta $)
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Duran, Ugur
AU - Acikgoz, Mehmet
AD - Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey
Y1 - 2017
PY - 2017
VL - 8
IS - 2
SP - 135
EP - 144
KW - Carlitz's $q$-Bernoulli polynomials
KW - Stirling numbers of the first kind
KW - Stirling numbers of the second kind
KW - $p$-adic $q$-integral
DO - 10.22075/ijnaa.2017.11767.1588
N2 - 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.
UR - https://ijnaa.semnan.ac.ir/article_2791.html
L1 - https://ijnaa.semnan.ac.ir/article_2791_48a0eba5d8560ea93b810f1b3562b4eb.pdf
ER -