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Year 2023, Volume: 6 Issue: 1, 19 - 30, 31.03.2023
https://doi.org/10.33434/cams.1215757

Abstract

References

  • [1] N. Acala, A unification of the generalized multiparameter Apostol-type Bernoulli, Euler, Fubini, and Genocchi polynomials of higher order, Eur. J. Pure Appl. Math., 13(3) (2020), 587-607.
  • [2] 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(5) (2017), 1605-1621.
  • [3] H. Ozden, Y. Simsek, H. M. Srivastava, A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials, Comput. Math. Appl., 60(10) (2010), 2779-2787.
  • [4] Y. Simsek, Computation methods for combinatorial sums and Euler type numbers related to new families of numbers, Math. Methods Appl. Sci., 40(7) (2017), 2347-2361.
  • [5] Y. Simsek, New families of special numbers for computing negative order Euler numbers and related numbers and polynomials, Appl. Anal. Discrete Math., 12 (2018), 1-35.
  • [6] H. M. Srivastava, R. Srivastava, A. Muhyi, G. Yasmin, H. Islahi, S. Araci, Construction of a new family of Fubini-type polynomials and its applications, Adv. Differ. Equ., 36 (2021), 25 pages, https://doi.org/10.1186/s13662-020-03202-x.
  • [7] P. Agarwal, R. Agarwal, M. Ruzhansky, Special Functions and Analysis of Differential Equations, 1st ed.; CRC Press: Boca Raton, FL, USA, 2020.
  • [8] V. Akhmedova, E. Akhmedov, Selected Special Functions for Fundamental Physics, Springer Briefs in Physics; Springer: Cham, Switzerland, 2019.
  • [9] J. Seaborn, Hypergeometric Functions and Their Applications, Springer: New York, NY, USA, 1991.
  • [10] I. Sneddon, Special Functions of Mathematical Physics and Chemistry, Oliver and Boyd: Edinburgh, UK, 1956.
  • [11] F. Qi, Diagonal recurrence relations, inequalities, and monotonicity related to the Stirling numbers of the second kind, Math. Inequal. Appl., 19(1) (2016), 313-323.
  • [12] O. A. Gross, Preferential arrangements, Amer. Math. Monthly, 69 (1962), 4-8.
  • [13] R. D. James, The factors of a square-free integer, Canad. Math. Bull., 11 (1968), 733-735.
  • [14] S. M. Tanny, On some numbers related to the Bell numbers, Canad. Math. Bull., 17(5) (1974/75), 733-738.
  • [15] K. N. Boyadzhiev, A series transformation formula and related polynomials, Int. J. Math. Math. Sci., 3(23) (2005), 3849-3866.
  • [16] L. Kargın, Some formulae for products of Fubini polynomials with applications, arXiv preprint (2016), available online at https://arxiv.org/abs/1701.01023.
  • [17] D. S. Kim, T. Kim, H.-I. Kwon, J.-W. Park, Two variable higher-order Fubini polynomials, J. Korean Math. Soc., 55(4) (2018), 975-986.
  • [18] F. Qi, On generalized Fubini polynomials, HAL preprint (2018), available online at https://hal. archives-ouvertes.fr/hal- 01853686v1. ̈ [19] H. M. Srivastava, M. A. Ozarslan, C. Kaanog ̆lu, Some Generalized Lagrange-Based Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, Russian J. Math. Phys., 20(1) (2013), 110-120.
  • [20] N. Ozmen, Some new properties of the Meixner polynomials, Sakarya University Journal of Science, 21(6) (2017), 1454-1462.
  • [21] N. Ozmen, E. Erkus-Duman, Some families of generating functions for the generalized Cesa ́ro polynomials, J. Comput. Anal. Appl., 25(4) (2018), 670–683.
  • [22] L. Carlitz, Some polynomials related to the Bernoulli and Euler polynomials, Utilitas Math., 19 (1981), 81-127.
  • [23] G.-W. Jang, T. Kim, Some identities of ordered Bell numbers arising from differential equations, Adv. Stud. Contemp. Math. (Kyungshang), 27(3) (2017), 385-397.
  • [24] N. Kilar, Y. Simsek, A new family of Fubini type numbers and polynomials associated with Apostol-Bernoulli numbers and polynomilas, J. Korean Math. Soc., 54(5) (2017), 1605-1621.
  • [25] T. Kim, Identities involving Laguerre polynomials derived from umbral calculus, Russ. J. Math. Phys., 21(1) (2014), 36-45.
  • [26] T. Kim, Degenerate ordered Bell numbers and polynomials, Proc. Jangjeon Math. Soc., 20(2) (2017), 137-144.
  • [27] B. Kurt, Y. Simsek, On the generalized Apostol-type Frobenius-Euler polynomials, Adv. Differ. Equ, 2013(1) (2013), 9 pages, doi:10.1186/1687-1847-2013-1.
  • [28] W. A. Khan, M. S. Abouzaid, A. H. Abusufian, K. S. Nisar, Some new classes of generalized Lagrange-based Apostol type Hermite polynomials, . J. Inequal. Spec. Funct., 10(1) (2019), 1-11.

Miscellaneous Properties of Generalized Fubini Polynomials

Year 2023, Volume: 6 Issue: 1, 19 - 30, 31.03.2023
https://doi.org/10.33434/cams.1215757

Abstract

This article attempts to present the generalized Fubini polynomials $F_{n}(x,y,z,q)$. The results obtained here include various families of multilinear and multilateral generating functions, various properties, as well as some special cases for these generalized Fubini polynomials $F_{n}(x,y,z,q)$. Finally, we get several interesting results of this generalized Fubini polynomials and obtain an integral representation.

References

  • [1] N. Acala, A unification of the generalized multiparameter Apostol-type Bernoulli, Euler, Fubini, and Genocchi polynomials of higher order, Eur. J. Pure Appl. Math., 13(3) (2020), 587-607.
  • [2] 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(5) (2017), 1605-1621.
  • [3] H. Ozden, Y. Simsek, H. M. Srivastava, A unified presentation of the generating functions of the generalized Bernoulli, Euler and Genocchi polynomials, Comput. Math. Appl., 60(10) (2010), 2779-2787.
  • [4] Y. Simsek, Computation methods for combinatorial sums and Euler type numbers related to new families of numbers, Math. Methods Appl. Sci., 40(7) (2017), 2347-2361.
  • [5] Y. Simsek, New families of special numbers for computing negative order Euler numbers and related numbers and polynomials, Appl. Anal. Discrete Math., 12 (2018), 1-35.
  • [6] H. M. Srivastava, R. Srivastava, A. Muhyi, G. Yasmin, H. Islahi, S. Araci, Construction of a new family of Fubini-type polynomials and its applications, Adv. Differ. Equ., 36 (2021), 25 pages, https://doi.org/10.1186/s13662-020-03202-x.
  • [7] P. Agarwal, R. Agarwal, M. Ruzhansky, Special Functions and Analysis of Differential Equations, 1st ed.; CRC Press: Boca Raton, FL, USA, 2020.
  • [8] V. Akhmedova, E. Akhmedov, Selected Special Functions for Fundamental Physics, Springer Briefs in Physics; Springer: Cham, Switzerland, 2019.
  • [9] J. Seaborn, Hypergeometric Functions and Their Applications, Springer: New York, NY, USA, 1991.
  • [10] I. Sneddon, Special Functions of Mathematical Physics and Chemistry, Oliver and Boyd: Edinburgh, UK, 1956.
  • [11] F. Qi, Diagonal recurrence relations, inequalities, and monotonicity related to the Stirling numbers of the second kind, Math. Inequal. Appl., 19(1) (2016), 313-323.
  • [12] O. A. Gross, Preferential arrangements, Amer. Math. Monthly, 69 (1962), 4-8.
  • [13] R. D. James, The factors of a square-free integer, Canad. Math. Bull., 11 (1968), 733-735.
  • [14] S. M. Tanny, On some numbers related to the Bell numbers, Canad. Math. Bull., 17(5) (1974/75), 733-738.
  • [15] K. N. Boyadzhiev, A series transformation formula and related polynomials, Int. J. Math. Math. Sci., 3(23) (2005), 3849-3866.
  • [16] L. Kargın, Some formulae for products of Fubini polynomials with applications, arXiv preprint (2016), available online at https://arxiv.org/abs/1701.01023.
  • [17] D. S. Kim, T. Kim, H.-I. Kwon, J.-W. Park, Two variable higher-order Fubini polynomials, J. Korean Math. Soc., 55(4) (2018), 975-986.
  • [18] F. Qi, On generalized Fubini polynomials, HAL preprint (2018), available online at https://hal. archives-ouvertes.fr/hal- 01853686v1. ̈ [19] H. M. Srivastava, M. A. Ozarslan, C. Kaanog ̆lu, Some Generalized Lagrange-Based Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, Russian J. Math. Phys., 20(1) (2013), 110-120.
  • [20] N. Ozmen, Some new properties of the Meixner polynomials, Sakarya University Journal of Science, 21(6) (2017), 1454-1462.
  • [21] N. Ozmen, E. Erkus-Duman, Some families of generating functions for the generalized Cesa ́ro polynomials, J. Comput. Anal. Appl., 25(4) (2018), 670–683.
  • [22] L. Carlitz, Some polynomials related to the Bernoulli and Euler polynomials, Utilitas Math., 19 (1981), 81-127.
  • [23] G.-W. Jang, T. Kim, Some identities of ordered Bell numbers arising from differential equations, Adv. Stud. Contemp. Math. (Kyungshang), 27(3) (2017), 385-397.
  • [24] N. Kilar, Y. Simsek, A new family of Fubini type numbers and polynomials associated with Apostol-Bernoulli numbers and polynomilas, J. Korean Math. Soc., 54(5) (2017), 1605-1621.
  • [25] T. Kim, Identities involving Laguerre polynomials derived from umbral calculus, Russ. J. Math. Phys., 21(1) (2014), 36-45.
  • [26] T. Kim, Degenerate ordered Bell numbers and polynomials, Proc. Jangjeon Math. Soc., 20(2) (2017), 137-144.
  • [27] B. Kurt, Y. Simsek, On the generalized Apostol-type Frobenius-Euler polynomials, Adv. Differ. Equ, 2013(1) (2013), 9 pages, doi:10.1186/1687-1847-2013-1.
  • [28] W. A. Khan, M. S. Abouzaid, A. H. Abusufian, K. S. Nisar, Some new classes of generalized Lagrange-based Apostol type Hermite polynomials, . J. Inequal. Spec. Funct., 10(1) (2019), 1-11.
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Muhammet Ağca This is me 0000-0003-1818-3098

Nejla Özmen 0000-0001-7555-1964

Publication Date March 31, 2023
Submission Date December 7, 2022
Acceptance Date January 24, 2023
Published in Issue Year 2023 Volume: 6 Issue: 1

Cite

APA Ağca, M., & Özmen, N. (2023). Miscellaneous Properties of Generalized Fubini Polynomials. Communications in Advanced Mathematical Sciences, 6(1), 19-30. https://doi.org/10.33434/cams.1215757
AMA Ağca M, Özmen N. Miscellaneous Properties of Generalized Fubini Polynomials. Communications in Advanced Mathematical Sciences. March 2023;6(1):19-30. doi:10.33434/cams.1215757
Chicago Ağca, Muhammet, and Nejla Özmen. “Miscellaneous Properties of Generalized Fubini Polynomials”. Communications in Advanced Mathematical Sciences 6, no. 1 (March 2023): 19-30. https://doi.org/10.33434/cams.1215757.
EndNote Ağca M, Özmen N (March 1, 2023) Miscellaneous Properties of Generalized Fubini Polynomials. Communications in Advanced Mathematical Sciences 6 1 19–30.
IEEE M. Ağca and N. Özmen, “Miscellaneous Properties of Generalized Fubini Polynomials”, Communications in Advanced Mathematical Sciences, vol. 6, no. 1, pp. 19–30, 2023, doi: 10.33434/cams.1215757.
ISNAD Ağca, Muhammet - Özmen, Nejla. “Miscellaneous Properties of Generalized Fubini Polynomials”. Communications in Advanced Mathematical Sciences 6/1 (March 2023), 19-30. https://doi.org/10.33434/cams.1215757.
JAMA Ağca M, Özmen N. Miscellaneous Properties of Generalized Fubini Polynomials. Communications in Advanced Mathematical Sciences. 2023;6:19–30.
MLA Ağca, Muhammet and Nejla Özmen. “Miscellaneous Properties of Generalized Fubini Polynomials”. Communications in Advanced Mathematical Sciences, vol. 6, no. 1, 2023, pp. 19-30, doi:10.33434/cams.1215757.
Vancouver Ağca M, Özmen N. Miscellaneous Properties of Generalized Fubini Polynomials. Communications in Advanced Mathematical Sciences. 2023;6(1):19-30.

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