[1] K. N. Boyadzhiev, A series transformation formula and related polynomials, Int. J.
Math. Math. Sci. (23), 3849–3866, 2005.
[2] K. N. Boyadzhiev and A. Dil, Geometric polynomials: properties and applications to
series with zeta values, Anal. Math. 42 (3), 203–224, 2016.
[3] A. Z. Broder, The r-Stirling numbers, Discrete Math. 49 (3), 241–259, 1984.
[4] L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math. 15,
51–88, 1979.
[5] K.-W. Chen, Algorithms for Bernoulli numbers and Euler numbers, J. Integer Seq. 4
(1), Article 01.1.6, 7, 2001.
[6] A. Dil and V. Kurt, Investigating geometric and exponential polynomials with Euler-
Seidel matrices, J. Integer Seq. 14(4), Article 11.4.6, 12, 2011.
[7] R. L. Graham, D. E. Knuth and O. Patashnik, Concrete mathematics, Addison-
Wesley Publishing Company, second edition, Reading, MA, 1994.
[8] L. Kargın, Some formulae for products of geometric polynomials with applications, J.
Integer Seq. 20(4), Art. 17.4.4, 15, 2017.
[9] L. Kargın, p-Bernoulli and geometric polynomials, Int. J. Number Theory 14 (2),
595–613, 2018.
[10] T. Kim, D. S. Kim and G.-W. Jang, A note on degenerate Fubini polynomials, Proc.
Jangjeon Math. Soc. 20(4), 521–531, 2017.
[11] F. Qi, Determinantal expressions and recurrence relations for Fubini and Eulerian
polynomials, Journal of Interdisciplinary Mathematics 22 (3), Art. 4, 18, 2019.
[12] H. M. Srivastava, M. A. Boutiche and M. Rahmani, A class of Frobenius-type Eulerian
polynomials, Rocky Mountain J. Math. 48 (3), 1003–1013, 2018.
[13] G. Tomaz and H. R. Malonek, Matrix approach to Frobenius-Euler polynomials, In
Computational science and its applications-ICCSA 2014. Part I, volume 8579 of
Lecture Notes in Comput. Sci. pages 75–86. Springer, Cham, 2014.
In the present paper, we define the generalized Kwang-Wu Chen matrix. Basic properties of this generalization, such as explicit formulas and generating functions are presented. Moreover, we focus on a new class of generalized Fubini polynomials. Then we discuss their relationship with other polynomials such as Fubini, Bell, Eulerian and Frobenius-Euler polynomials. We have also investigated some basic properties related to the degenerate generalized Fubini polynomials.
[1] K. N. Boyadzhiev, A series transformation formula and related polynomials, Int. J.
Math. Math. Sci. (23), 3849–3866, 2005.
[2] K. N. Boyadzhiev and A. Dil, Geometric polynomials: properties and applications to
series with zeta values, Anal. Math. 42 (3), 203–224, 2016.
[3] A. Z. Broder, The r-Stirling numbers, Discrete Math. 49 (3), 241–259, 1984.
[4] L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math. 15,
51–88, 1979.
[5] K.-W. Chen, Algorithms for Bernoulli numbers and Euler numbers, J. Integer Seq. 4
(1), Article 01.1.6, 7, 2001.
[6] A. Dil and V. Kurt, Investigating geometric and exponential polynomials with Euler-
Seidel matrices, J. Integer Seq. 14(4), Article 11.4.6, 12, 2011.
[7] R. L. Graham, D. E. Knuth and O. Patashnik, Concrete mathematics, Addison-
Wesley Publishing Company, second edition, Reading, MA, 1994.
[8] L. Kargın, Some formulae for products of geometric polynomials with applications, J.
Integer Seq. 20(4), Art. 17.4.4, 15, 2017.
[9] L. Kargın, p-Bernoulli and geometric polynomials, Int. J. Number Theory 14 (2),
595–613, 2018.
[10] T. Kim, D. S. Kim and G.-W. Jang, A note on degenerate Fubini polynomials, Proc.
Jangjeon Math. Soc. 20(4), 521–531, 2017.
[11] F. Qi, Determinantal expressions and recurrence relations for Fubini and Eulerian
polynomials, Journal of Interdisciplinary Mathematics 22 (3), Art. 4, 18, 2019.
[12] H. M. Srivastava, M. A. Boutiche and M. Rahmani, A class of Frobenius-type Eulerian
polynomials, Rocky Mountain J. Math. 48 (3), 1003–1013, 2018.
[13] G. Tomaz and H. R. Malonek, Matrix approach to Frobenius-Euler polynomials, In
Computational science and its applications-ICCSA 2014. Part I, volume 8579 of
Lecture Notes in Comput. Sci. pages 75–86. Springer, Cham, 2014.
Sebaoui, M., Laissaoui, D., Guettaı, G., Rahmani, M. (2023). Generalized Fubini transform with two variables. Hacettepe Journal of Mathematics and Statistics, 52(4), 931-944. https://doi.org/10.15672/hujms.1139692
AMA
Sebaoui M, Laissaoui D, Guettaı G, Rahmani M. Generalized Fubini transform with two variables. Hacettepe Journal of Mathematics and Statistics. August 2023;52(4):931-944. doi:10.15672/hujms.1139692
Chicago
Sebaoui, Madjid, Diffalah Laissaoui, Ghania Guettaı, and Mourad Rahmani. “Generalized Fubini Transform With Two Variables”. Hacettepe Journal of Mathematics and Statistics 52, no. 4 (August 2023): 931-44. https://doi.org/10.15672/hujms.1139692.
EndNote
Sebaoui M, Laissaoui D, Guettaı G, Rahmani M (August 1, 2023) Generalized Fubini transform with two variables. Hacettepe Journal of Mathematics and Statistics 52 4 931–944.
IEEE
M. Sebaoui, D. Laissaoui, G. Guettaı, and M. Rahmani, “Generalized Fubini transform with two variables”, Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 4, pp. 931–944, 2023, doi: 10.15672/hujms.1139692.
ISNAD
Sebaoui, Madjid et al. “Generalized Fubini Transform With Two Variables”. Hacettepe Journal of Mathematics and Statistics 52/4 (August 2023), 931-944. https://doi.org/10.15672/hujms.1139692.
JAMA
Sebaoui M, Laissaoui D, Guettaı G, Rahmani M. Generalized Fubini transform with two variables. Hacettepe Journal of Mathematics and Statistics. 2023;52:931–944.
MLA
Sebaoui, Madjid et al. “Generalized Fubini Transform With Two Variables”. Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 4, 2023, pp. 931-44, doi:10.15672/hujms.1139692.
Vancouver
Sebaoui M, Laissaoui D, Guettaı G, Rahmani M. Generalized Fubini transform with two variables. Hacettepe Journal of Mathematics and Statistics. 2023;52(4):931-44.