cA \(q\)-analogue of generalized translated Whitney numbers: Cigler's approach
Volume 24, Issue 1, pp 82--96
http://dx.doi.org/10.22436/jmcs.024.01.08
Publication Date: January 18, 2021
Submission Date: August 26, 2020
Revision Date: December 03, 2020
Accteptance Date: December 12, 2020
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Authors
Roberto B. Corcino
- Research Institute for Computational Mathematics and Physics, Cebu Normal University, Cebu City 6000, Philippines.
Jezer C. Fernandez
- Department of Mathematics, Mindanao State University, Marawi City 9700, Philippines.
Mary Ann Ritzell P. Vega
- Department of Mathematics and Statistics, College of Science and Mathematics, Mindanao State University-Iligan Institute of Technology, Iligan City 9200, Philippines.
Abstract
Using a certain combinatorial interpretation in terms of set partition, a \(q\)-analogue of generalized translated Whitney numbers of the second kind is defined in this paper. Some properties such as the recurrence relation, explicit formula, and certain symmetric formula are obtained. Moreover, a \(q\)-analogue of generalized translated Whitney numbers of the first kind is introduced to obtain a \(q\)-analogue of the orthogonality and inverse relations of the two kinds of generalized translated Whitney numbers.
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ISRP Style
Roberto B. Corcino, Jezer C. Fernandez, Mary Ann Ritzell P. Vega, cA \(q\)-analogue of generalized translated Whitney numbers: Cigler's approach, Journal of Mathematics and Computer Science, 24 (2022), no. 1, 82--96
AMA Style
Corcino Roberto B., Fernandez Jezer C., Vega Mary Ann Ritzell P., cA \(q\)-analogue of generalized translated Whitney numbers: Cigler's approach. J Math Comput SCI-JM. (2022); 24(1):82--96
Chicago/Turabian Style
Corcino, Roberto B., Fernandez, Jezer C., Vega, Mary Ann Ritzell P.. "cA \(q\)-analogue of generalized translated Whitney numbers: Cigler's approach." Journal of Mathematics and Computer Science, 24, no. 1 (2022): 82--96
Keywords
- Stirling numbers
- \(r\)-Stirling numbers
- translated Whitney numbers
- \(q\)-binomial coefficients
- \(q\)-factorial
MSC
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