TY - JOUR T1 - Generalized Fubini transform with two variables AU - Sebaoui, Madjid AU - Laissaoui, Diffalah AU - Guettaı, Ghania AU - Rahmani, Mourad PY - 2023 DA - August DO - 10.15672/hujms.1139692 JF - Hacettepe Journal of Mathematics and Statistics PB - Hacettepe University WT - DergiPark SN - 2651-477X SP - 931 EP - 944 VL - 52 IS - 4 LA - en AB - 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. KW - Bell polynomials KW - degenerate generalized Fubini polynomials KW - Eulerian polynomials KW - explicit formulas KW - Fubini transform KW - Fubini polynomials KW - Frobenius-Euler polynomials KW - generating functions KW - probabilistic representation KW - random variable KW - Stirling numbers CR - [1] K. N. Boyadzhiev, A series transformation formula and related polynomials, Int. J. Math. Math. Sci. (23), 3849–3866, 2005. CR - [2] K. N. Boyadzhiev and A. Dil, Geometric polynomials: properties and applications to series with zeta values, Anal. Math. 42 (3), 203–224, 2016. CR - [3] A. Z. Broder, The r-Stirling numbers, Discrete Math. 49 (3), 241–259, 1984. CR - [4] L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math. 15, 51–88, 1979. CR - [5] K.-W. Chen, Algorithms for Bernoulli numbers and Euler numbers, J. Integer Seq. 4 (1), Article 01.1.6, 7, 2001. CR - [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. CR - [7] R. L. Graham, D. E. Knuth and O. Patashnik, Concrete mathematics, Addison- Wesley Publishing Company, second edition, Reading, MA, 1994. CR - [8] L. Kargın, Some formulae for products of geometric polynomials with applications, J. Integer Seq. 20(4), Art. 17.4.4, 15, 2017. CR - [9] L. Kargın, p-Bernoulli and geometric polynomials, Int. J. Number Theory 14 (2), 595–613, 2018. CR - [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. CR - [11] F. Qi, Determinantal expressions and recurrence relations for Fubini and Eulerian polynomials, Journal of Interdisciplinary Mathematics 22 (3), Art. 4, 18, 2019. CR - [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. CR - [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. UR - https://doi.org/10.15672/hujms.1139692 L1 - https://dergipark.org.tr/en/download/article-file/2521986 ER -