Research Article
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Year 2023, , 931 - 944, 15.08.2023
https://doi.org/10.15672/hujms.1139692

Abstract

References

  • [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.

Generalized Fubini transform with two variables

Year 2023, , 931 - 944, 15.08.2023
https://doi.org/10.15672/hujms.1139692

Abstract

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.

References

  • [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.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Madjid Sebaoui 0000-0002-4918-8206

Diffalah Laissaoui 0000-0002-6453-4453

Ghania Guettaı 0000-0003-0320-1150

Mourad Rahmani 0000-0003-3097-6381

Publication Date August 15, 2023
Published in Issue Year 2023

Cite

APA 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.