A Note on Central Bell Numbers and Polynomials
Tóm tắt
Từ khóa
Tài liệu tham khảo
P. L. Butzer, M. Schmidt, E. L. Stark, and L. Vogt, “Central Factorial Numbers, Their Main Properties and Some Applications,” Numer. Funct. Anal. Optim. 10, 419–488 (1989).
L. Carlitz and J. Riordan, “The Divided Central Differences of Zero,” Canad. J. Math. 15, 94–100 (1963).
C. H. Chang and C. W. Ha, “Central Factorial Numbers and Values of Bernoulli and Euler Polynomials at Rationals,” Numer Funct. Anal. Optim. 30(3–4), 214–226 (2009).
L. Comtet, “Nombres de Stirling generaux et fonctions symetriques,” C. R. Acad. Sci. Paris Ser. A 275, 747–750 (1972).
L. Comtet, Advanced Combinatorics: the Art of Finite and Infinite Expansions (translated from the French by J.W. Nienhuys) (Reidel, Dordrecht and Boston, 1974).
D. V. Dolgy and T. Kim, Some Explicit Formulas of Degenerate Stirling Numbers Associated with the Degenerate Special Numbers and Polynomials, Proc. Jangjeon Math. Soc. 21(2), 309–317 (2018).
D. V. Dolgy, T. Kim, H.-I. Kwon, and J. J. Seo, “Some Identities for Degenerate Euler Numbers and Polynomials Arising from Degenerate Bell Polynomials,” Proc. Jangjeon Math. Soc. 19(3), 457–464 (2016).
G.-W. Jang, T. Kim, and H.-I. Kwon, “On the Extension of Degenerate Stirling Polynomials of the Second Kind and Degenerate Bell Polynomials,” Adv. Stud. Contemp. Math. (Kyungshang) 28(2), 305–316 (2018).
C. Jordan, Calculus of Finite Differences (Chelsea, New York, 1960).
D. S. Kim and T. Kim, “Some Identities of Bell Polynomials,” Sci. China Ser A 58(10), 2095–2104 (2015).
D. S. Kim, T. Kim, and G.-W. Jang, “Some Identities of Partially Degenerate Touchard Polynomials Arising from Differential Equations,” Adv. Stud. Contemp. Math. (Kyungshang) 27(2), 243–251 (2017).
T. Kim, “A Note on Ordered Bell Numbers and Polynomials,” Adv. Stud. Contemp. Math. (Kyungshang) 27(2), 289–298 (2017).
T. Kim, “A Note on Degenerate Stirling Polynomials of the Second Kind,” Proc. Jangjeon Math. Soc. 20(3), 319–331 (2017).
T. Kim, J. Choi, and Y.-H. Kim, “Some Identities on the q-Bernstein Polynomials, q-Stirling Numbers and q-Bernoulli Numbers,” Adv. Stud. Contemp. Math. (Kyungshang) 20(3), 335–341 (2010).
T. Kim and G.-W. Jang, “A Note on Degenerate Gamma Function and Degenerate Stirling Number of the Second Kind,” Adv. Stud. Contemp. Math. (Kyungshang) 28(2), 207–214 (2018).
T. Kim, D. S. Kim, and G.-W. Jang, “Extended Stirling Polynomials of the Second Kind and Extended Bell Polynomials,” Proc. Jangjeon Math. Soc. 20(3), 365–376 (2017).
T. Kim and D. S. Kim, Identities for Degenerate Bernoulli Polynomials and Korobov Polynomials of the First Kind (Science China-Mathematics https://doi.org/10.1007/s11425-018-9338-5 (in press) (see: http://engine.scichina.com/publisher/scp/journal/SCM/doi/10.1007/s11425-018-9338-5?slug=abstract)).
A. K. Kwasniewski, “On ψ-Umbral Extensions of Stirling Numbers and Dobinski-Like Formulas,” Adv. Stud. Contemp. Math. (Kyungshang) 16(1), 73–100 (2006).
J. Riordan, Combinatorial Identities (Wiley, New York, 1968).
S. Roman, The Umbral Calculus (Academic Press, New York, 1984).