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International Journal of Nonlinear Analysis and Applications
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Volume Volume 8 (2017)
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Duran, U., Acikgoz, M. (2017). Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($\alpha ,\beta $). International Journal of Nonlinear Analysis and Applications, 8(2), 135-144. doi: 10.22075/ijnaa.2017.11767.1588
Ugur Duran; Mehmet Acikgoz. "Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($\alpha ,\beta $)". International Journal of Nonlinear Analysis and Applications, 8, 2, 2017, 135-144. doi: 10.22075/ijnaa.2017.11767.1588
Duran, U., Acikgoz, M. (2017). 'Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($\alpha ,\beta $)', International Journal of Nonlinear Analysis and Applications, 8(2), pp. 135-144. doi: 10.22075/ijnaa.2017.11767.1588
Duran, U., Acikgoz, M. Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($\alpha ,\beta $). International Journal of Nonlinear Analysis and Applications, 2017; 8(2): 135-144. doi: 10.22075/ijnaa.2017.11767.1588

Modified degenerate Carlitz's $q$-bernoulli polynomials and numbers with weight ($\alpha ,\beta $)

Article 13, Volume 8, Issue 2, Summer and Autumn 2017, Page 135-144  XML PDF (375 K)
Document Type: Research Paper
DOI: 10.22075/ijnaa.2017.11767.1588
Authors
Ugur Duran orcid ; Mehmet Acikgoz
Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, Gaziantep, 27310, Turkey
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
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