On F-Frobenius-Euler polynomials and their matrix approach
Volume 32, Issue 4, pp 377--386
http://dx.doi.org/10.22436/jmcs.032.04.07
Publication Date: November 03, 2023
Submission Date: June 26, 2023
Revision Date: July 10, 2023
Accteptance Date: September 06, 2023
Authors
A. Urieles
- Programa de Matematicas, Universidad del Atlantico, Km 7 Via Pto. Colombia, Barranquilla, Colombia .
William Ramirez
- Universitá Telematica Internazionale Uninettuno, Rome, Italy.
- Departamento de Ciencias Naturales y Exactas, Universidad de la Costa, , Barranquilla, Colombia .
L. C. Perez H
- Programa de Matematicas, Universidad del Atlantico, Km 7 Via Pto. Colombia, Barranquilla, Colombia .
M. J. Ortega
- Departamento de Ciencias Naturales y Exactas, Universidad de la Costa, Barranquilla, Colombia .
J. Arenas-Penaloza
- Departamento de Ciencias Naturales y Exactas, Universidad de la Costa, Barranquilla, Colombia .
Abstract
In this article, the generalized F-Frobenius-Euler polynomials \(H_{n,F}^{(\alpha)}(x;\mu)\) are introduced, through their generating function, and properties are established for these generalized polynomials. In addition, we define the generalized polynomial Fibo-Frobenius-Euler matrix \(\mathcal{H}^{(\alpha)}_{n}(x,F,\mu)\). Factorizations of the Fibo-Frobenius-Euler polynomial matrix are established with the generalized Fibo-Pascal matrix and the Fibonacci matrix. The inverse of the Fibo-Frobenius-Euler matrix is also found.
Share and Cite
ISRP Style
A. Urieles, William Ramirez, L. C. Perez H, M. J. Ortega, J. Arenas-Penaloza, On F-Frobenius-Euler polynomials and their matrix approach, Journal of Mathematics and Computer Science, 32 (2024), no. 4, 377--386
AMA Style
Urieles A., Ramirez William, Perez H L. C., Ortega M. J., Arenas-Penaloza J., On F-Frobenius-Euler polynomials and their matrix approach. J Math Comput SCI-JM. (2024); 32(4):377--386
Chicago/Turabian Style
Urieles, A., Ramirez, William, Perez H, L. C., Ortega, M. J., Arenas-Penaloza, J.. "On F-Frobenius-Euler polynomials and their matrix approach." Journal of Mathematics and Computer Science, 32, no. 4 (2024): 377--386
Keywords
- Euler polynomials
- F-Frobenius-Euler polynomials
- Euler matrix
- generalized Euler matrix
- generalized Pascal matrix
- Fibonacci matrix
- Lucas matrix
MSC
References
-
[1]
D. Bedoya, C. Cesarano, S. D´ıaz, R. Ram´ırez, New Classes of Degenerate Unified Polynomials, Axioms, 10 (2023), 1–10
-
[2]
G. S. Call, D. J Velleman, Pascal’s matrices, Amer. Math. Monthly, 100 (1993), 372–376
-
[3]
C. Cesarano, W. Ram´ırez, S. D´ıaz, A. Shamaoon, W. A Khan, On Apostol–Type Hermite Degenerated Polynomials, Mathematics, 11 (2013), 1–13
-
[4]
L. Comtet, Advanced Combinatorics. The Art of Finite and Infinite Expansions, D. Reidel Publishing Co., Dordrecht- Holland/Boston (1974)
-
[5]
E. Krot, An introduction to finite Fibonomial calculus, Cent. Eur. J. Math., 2 (2004), 754–766
-
[6]
S. Kus¸, N. Tugla, T. Kim, Bernoulli F-polynomials and Fibo-Bernoulli matrices, Adv. Differ. Equ., 2019 (2019), 16 pages
-
[7]
G.-Y. Lee, J.-S. Kim, S.-G. Lee, Factorizations and eigenvalues of Fibonacci and symmetric Fibonacci matrices, Fibonacci Quart., 40 (2002), 203–211
-
[8]
M. J. Ortega, W. Ram´ırez, A. Urieles, New generalized Apostol-Frobenius-Euler polynomials and their matrix approach, Kragujevac J. Math., 45 (2021), 393–407
-
[9]
Y. Quintana, W. Ram´ırez, A. Urieles, On an operational matrix method based on generalized Bernoulli polynomials of level m, Calcolo, 55 (2018), 29 pages
-
[10]
Y. Quintana, W. Ram´ırez, A. Urieles, Euler matrices and their algebraic properties revisited, Appl. Math. Inf. Sci., 14 (2020), 583–596
-
[11]
W. Ram´ırez, C. Cesarano, Some new classes of degenerated generalized Apostol-Bernoulli, Apostol-Euler and Apostol- Genocchi polynomials, Carpathian Math. Publ., 14 (2022), 354–363
-
[12]
W. Ram´ırez, C. Cesarano, S. D´ıaz, New results for degenerated generalized Apostol-Bernoulli, Apostol-Euler and Apostol- Genocchi polynomials, WSEAS Trans. Math., 21 (2022), 604–608
-
[13]
J. Riordan, Combinatorial identities, John Wiley & Sons, New York-London-Sydney (1968)
-
[14]
A. Urieles, W. Ram´ırez, M. J. Ortega, D. Bedoya, Fourier expansion and integral representation generalized Apostol-type Frobenius-Euler polynomials, Adv. Differ. Equ., 2020 (2020), 14 pages
-
[15]
Z. Zhang, The linear algebra of generalized Pascal matrix, Linear Algebra Appl., 250 (1994), 51–60
-
[16]
Z. Zhang, M. Liu, An extension of generalized Pascal matrix and its algebraic properties, Linear Algebra Appl., 271 (1998), 169–177
-
[17]
Z. Zhang, J. Wang, Bernoulli matrix and its algebraic properties, Discrete Appl. Math., 154 (2006), 1622–1632
