On the degenerate higher order Frobenius-Euler polynomials
Volume 34, Issue 4, pp 404--423
https://dx.doi.org/10.22436/jmcs.034.04.07
Publication Date: April 10, 2024
Submission Date: January 13, 2024
Revision Date: February 14, 2024
Accteptance Date: February 21, 2024
Authors
J. Kwon
- Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Republic of Korea.
J.-W. Park
- Department of Mathematics Education, Daegu University, 38453, Republic of Korea.
Abstract
Degenerate versions of special numbers, originating from the work of L. Carlitz, play a crucial role in various fields, including pure and applied mathematics, com-
binatorics, number theory, and mathematical physics. They are actively under investigation by numerous researchers.
Recently, [D. S. Kim, T. Kim, J. Math. Anal. Appl., \(\bf 493\) (2021), 21 pages] introduced the \(\lambda\)-umbral calculus as a research tool specifically for degenerate special polynomials, utilizing it to establish connections between special polynomials and their degenerate counterparts.
In this paper, we investigate the relationships between degenerate Frobenius-Euler polynomials and other versions of degenerate special polynomials and numbers. By employing \(\lambda\)-umbral calculus, explicit formulas for Frobenius-Euler polynomials of order \(r\) are derived. The presented formulas reveal connections between these polynomials and well-known special numbers and polynomials. Additionally, the distribution patterns of the roots of these polynomials are examined.
Share and Cite
ISRP Style
J. Kwon, J.-W. Park, On the degenerate higher order Frobenius-Euler polynomials, Journal of Mathematics and Computer Science, 34 (2024), no. 4, 404--423
AMA Style
Kwon J., Park J.-W., On the degenerate higher order Frobenius-Euler polynomials. J Math Comput SCI-JM. (2024); 34(4):404--423
Chicago/Turabian Style
Kwon, J., Park, J.-W.. "On the degenerate higher order Frobenius-Euler polynomials." Journal of Mathematics and Computer Science, 34, no. 4 (2024): 404--423
Keywords
- Degenerate Frobenius-Euler polynomials
- umbral calculus
- \(\lambda\)-analogue of the Stirling numbers of the first kind
- \(\lambda\)-analogue of the Stirling numbers of the second kind
- degenerate polyexponential function
MSC
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