About family Apostol Fubini-Euler type polynomials: Fourier expansions and integral representation
Authors
A. Urieles
- Programa de Matemáticas, Universidad del Atlántico, Km 7 Via Pto, Colombia, Barranquilla, Colombia.
W. Ramirez
- Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy.
- Departamento de Ciencias Naturales y Exactas, Universidad de la Costa, Barranquilla, Colombia.
D. Bedoya
- Departamento de Ciencias Basicas, Universidad Metropolitana, Barranquilla, Colombia.
C. Cesarano
- Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy.
M. J. Ortega
- Departamento de Ciencias Naturales y Exactas, Universidad de la Costa, Barranquilla, Colombia.
Abstract
This paper introduces new families of Fubini-Euler type and Apostol Fubini-Euler type polynomials, providing expressions, recurrence relations, and identities. We also derive Fourier series, and integral representations, and present their rational argument representation.
Share and Cite
ISRP Style
A. Urieles, W. Ramirez, D. Bedoya, C. Cesarano, M. J. Ortega, About family Apostol Fubini-Euler type polynomials: Fourier expansions and integral representation, Journal of Mathematics and Computer Science, 35 (2024), no. 4, 457--470
AMA Style
Urieles A., Ramirez W., Bedoya D., Cesarano C., Ortega M. J., About family Apostol Fubini-Euler type polynomials: Fourier expansions and integral representation. J Math Comput SCI-JM. (2024); 35(4):457--470
Chicago/Turabian Style
Urieles, A., Ramirez, W., Bedoya, D., Cesarano, C., Ortega, M. J.. "About family Apostol Fubini-Euler type polynomials: Fourier expansions and integral representation." Journal of Mathematics and Computer Science, 35, no. 4 (2024): 457--470
Keywords
- Fubini-Euler polynomials
- Apostol Fubini-Euler type
- series of Fourier
- integral representation
MSC
References
-
[1]
M. Abdelhakem, D. Baleanu, P. Agarwal, M. Hanaa, Approximating system of ordinary differential-algebraic equations via derivative of Legendre polynomials operational matrices, Int. J. Mod. Phys. C, 34 (2023),
-
[2]
M. Abramowitz, I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, U. S. Government Printing Office, Washington, DC (1964)
-
[3]
P. Agarwal, F. Qi, M. Chand, S. Jain, Certain integrals involving the generalized hypergeometric function and the Laguerre polynomials, J. Comput. Appl. Math., 313 (2017), 307–317
-
[4]
S. Araci, M. Acikgoz, Construction of Fourier expansion of Apostol Frobenius-Euler polynomials and its applications, Adv. Difference Equ., 2018 (2018), 14 pages
-
[5]
D. Bedoya, M. Ortega, W. Ram´ırez, A. Urieles, New biparametric families of Apostol-Frobenius-Euler polynomials of level m, Mat. Stud., 55 (2021), 10–23
-
[6]
L. Castilla, W. Ram´ırez, A. Urieles, An extended generalized q-extensions for the Apostol type polynomials, Abstr. Appl. Anal., 2018 (2018), 13 pages
-
[7]
J. B. Conway, Functions of one complex variable, Springer-Verlag, New York-Berlin (1978)
-
[8]
C. B. Corcino, R. B. Corcino, Fourier expansions for higher-order Apostol-Genocchi, Apostol-Bernoulli and Apostol-Euler polynomials, Adv. Difference Equ., 2020 (2020), 13 pages
-
[9]
C. Corcino, R. Corcino, J. Casquejo, Fourier Series Expansion and Integral Representation of Apostol–Type Frobenius– Euler Polynomials of Complex Parameters and Order , Symmetry, 14 (2022), 13 pages
-
[10]
A. A. El-Sayed, P. Agarwal, Numerical solution of multiterm variable-order fractional differential equations via shifted Legendre polynomials, Math. Methods Appl. Sci., 42 (2019), 3978–3991
-
[11]
G. B. Follan, Fourier analysis and its applications, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA (1992)
-
[12]
I. J. Good, The number of orderings of n candidates when ties are permitted, Fibonacci Quart., 13 (1975), 11–18
-
[13]
W. A. Khan, A. Muhyi, R. Ali, K. A. H. Alzobydi, M. Singh, P. Agarwal, A new family of degenerate poly-Bernoulli polynomials of the second kind with its certain related properties, AIMS Math., 6 (2021), 12680–12697
-
[14]
N. Kilar, Y. Simsek, A new family of Fubini type numbers and polynomials associated with Apostol-Bernoulli numbers and polynomials, J. Korean Math. Soc., 54 (2017), 1605–1621
-
[15]
Q.-M. Luo, Fourier expansions and integral representations for the Apostol-Bernoulli and Apostol-Euler polynomials, Math. Comput., 78 (2009), 2193–2208
-
[16]
Q.-M. Luo, Extensions of the Genocchi polynomials and their Fourier expansions and integral representations, Osaka J. Math., 48 (2011), 291–309
-
[17]
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
-
[18]
A. Praveen, A. A. El-Sayed, Vieta-Lucas polynomials for solving a fractional-order mathematical physics model, Adv. Difference Equ., 2020 (2020), 18 pages
-
[19]
Y. Quintana, W. Ram´ırez, A. Urieles, Generalized Apostol-type polynomial matrix and its algebraic properties, Math. Rep. (Bucur.), 21 (2019), 249–264
-
[20]
Y. Quintana, W. Ram´ırez, A. Urieles, Euler matrices and their algebraic properties revisited, Appl. Math. Inf. Sci., 14 (2020), 583–596
-
[21]
A. Urieles, M. J. Ortega, W. Ram´ırez, S. Vega, New results on the q-generalized Bernoulli polynomials of level m, Demonstr. Math., 52 (2019), 511–522
-
[22]
A. Urieles, W. Ram´ırez, M. J. Ortega, D. Bedoya, Fourier expansion and integral representation generalized Apostol-type Frobenius-Euler polynomials, Adv. Difference Equ., 2020 (2020), 14 pages
