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Some identities related to degenerate Stirling numbers of the second kind

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Abstrakty
EN
The degenerate Stirling numbers of the second kind were introduced as a degenerate version of the ordinary Stirling numbers of the second kind. They appear very frequently when one studies various degenerate versions of some special numbers and polynomials. The aim of this article is to further study some identities and properties related to the degenerate Stirling numbers of the second kind, in connection with the degenerate Bell polynomials, the degenerate Fubini polynomials, the degenerate Bernoulli polynomials, and the degenerate Euler polynomials.
Wydawca
Rocznik
Strony
812--821
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
autor
  • Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
autor
  • Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea
  • Department Of Mathematics Education, Daegu Catholic University, Gyeongsan 38430, Republic of Korea
Bibliografia
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  • [3] S. Araci, A new class of Bernoulli polynomials attached to polyexponential functions and related identities. Adv. Stud. Contemp. Math. 31 (2021), no. 2, 195–204.
  • [4] M. Acikgoz and U. Duran, Unified degenerate central Bell polynomials. J. Math. Anal. 11 (2020), no. 2, 18–33.
  • [5] D. S. Kim and T. Kim, A note on a new type of degenerate Bernoulli numbers. Russ. J. Math. Phys. 27 (2020), no. 2, 227–235.
  • [6] D. S. Kim and T. Kim, Degenerate Sheffer sequences and λ -Sheffer sequences, J. Math. Anal. Appl. 493 (2021), no. 1, Paper No. 124521, 21 pp.
  • [7] T. Kim and D. S. Kim, Degenerate Laplace transform and degenerate gamma function, Russ. J. Math. Phys. 24 (2017), no. 2, 241–248.
  • [8] T. Kim and D. S. Kim, On some degenerate differential and degenerate difference operators. Russ. J. Math. Phys. 29 (2022), no. 1, 37–46.
  • [9] T. Kim, D. S. Kim, and D. V. Dolgy, On partially degenerate Bell numbers and polynomials. Proc. Jangjeon Math. Soc. 20 (2017), no. 3, 337–345.
  • [10] T. Kim, D. S. Kim, D. V. Dolgy, and J.-W. Park, Degenerate binomial and Poisson random variables associated with degenerate Lah-Bell polynomials. Open Math. 19 (2021), no. 1, 1588–1597.
  • [11] T. Kim, D. S. Kim, and H. K. Kim, Normal ordering of degenerate integral powers of number operator and its applications. Appl. Math. Sci. Eng. 30 (2022), no. 1, 440–447.
  • [12] T. Kim, D. S. Kim, and H. K. Kim, Some properties on degenerate Fubini polynomials. Appl. Math. Sci. Eng. 30 (2022), no. 1, 235–248.
  • [13] T. Kim, D. S. Kim, and J. Kwon, A series transformation formula and related degenerate polynomials. Adv. Stud. Contemp. Math. (Kyungshang) 32 (2022), no. 2, 121–136.
  • [14] T. Kim and D. S. Kim, Degenerate Whitney numbers of first and second kind of Dowling lattices. Russ. J. Math. Phys. 29 (2022), no. 3, 358–377.
  • [15] U. Duran, Degenerate Sumudu transform and its properties. Filomat 35 (2021), no. 14, 4731–4741.
  • [16] L. Comtet, Advanced combinatorics. The art of finite and infinite expansions, Revised and enlarged edition, D. Reidel Publishing Co., Dordrecht, 1974, xi+343 pp. ISBN: 90-277-0441-4.
  • [17] N. Kilar and Y. Simsek, Combinatorial sums involving Fubini type numbers and other special numbers and polynomials: approach trigonometric functions and p-adic integrals. Adv. Stud. Contemp. Math. (Kyungshang) 31 (2021), no. 1, 75–87.
  • [18] S. Roman, The umbral calculus, Pure and Applied Mathematics, vol. 111, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1984, x+193 pp.
  • [19] Y. Simsek, Miscellaneous formulae for the certain class of combinatorial sums and special numbers. Bull. Cl. Sci. Math. Nat. Sci. Math. No. 46 (2021), 151–167.
  • [20] T. Usman, M. Aman, O. Khan, K. S. Nisar, and S. Araci, Construction of partially degenerate Laguerre-Genocchi polynomials with their applications. AIMS Math. 5 (2020), no. 5, 4399–4411.
  • [21] J. Choi, N. Khan, T. Usman, and M. Aman, Certain unified polynomials, Integral Transforms Special Functions. 30 (2019), no. 1, 28–40, DOI: https://doi.org/10.1080/10652469.2018.1534847.
  • [22] N. Khan, M. Aman, T. Usman, and J. Choi, Legendre-Gould Hopper based Sheffer polynomials and operational methods. Symmetry (MDPI) 12 (2020)2051. DOI: https://doi.org/10.3390/sym12122051.
  • [23] T. Usman, M. Saif, and J. Choi, Certain identities associated with (p, q)-binomial coefficients and (p, q)-Stirling polynomials of the second kind, Symmetry (MDPI). 12 (2020), no. 9, 1436, DOI: https://doi.org/10.3390/sym12091436,112840.
  • [24] T. Usman, N. Khan, M. Aman, and J. Choi, A family of generalized Legendre-based Apostol-type polynomials, Axioms (MDPI) 11 (2022), no. 1, 29, DOI: https://doi.org/10.3390/axioms11010029.
  • [25] T. Usman, N. Khan, M. Aman, S. Al-Omari, K. Nonlaopon, and J. Choi, Some generalized properties of poly-Daehee numbers and polynomials based on Apostol-Genocchi polynomials, Mathematics (MDPI) 10 (2022), 2502, 1–15, DOI: https://doi.org/10.3390/math10142502.
Uwagi
PL
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-7f7ad6f7-6180-428b-ade7-1f26e0015c16
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