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2020, vol. 24, iss. 2, pp. 8398

New family of special numbers associated with finite operator
USTHB Algeirs, Faculty of Sciences, Department of Mathematics, Algebra and Number Theory Laboratory, TiziOuzou, Algeria
email: mouloud.goubi@ummto.dz
Abstract
Using the notion of the generating function of a function, we define an operator with whom we manage to build a large family of numbers and polynomials. This technique permits to give the closed formulae and interesting combinatorial identities. Among others, these polynomials are a generalization of the Fubini numbers and polynomials.



References


Baker, G.A.Jr. (1973) The existence and convergence of subsequences of Padé approximants. Journal of Mathematical Analysis and Applications, 43(2): 498528


Baker, G.A.Jr. (1975) Essentials of Padé Approximants. New York: Academic Press


Baker, G.A., GravesMorris, P.R. (1982) The convergence of sequences of Padé approximants. Journal of Mathematical Analysis and Applications, 87(2): 382394


Chen, K.W. (2007) Inversion of Generating Functions using Determinants. Journal of Integer Sequences, 10 (10), Article ID: 07.10.5, 10 pages


Cheney, E.W., Sharma, A. (1964) Bernstein Power Series. Canadian Journal of Mathematics, 16: 241252

1

Comtet, L. (1974) Advanced Combinatorics: The Art of Finite and Infinite Expansions. DordrechtBoston: D. Reidel Publishing Co, Revised and Enlarged Edition


Corcino, C.B., Corcino, R.B., Mező, I., Ramírez, J.L. (2018) Some polynomials associated with the rWhitney numbers. Proceedings  Mathematical Sciences, 128(3): 128128


Faà, di B.F. (1855) Sullo Sviluppo delle funzioni. Annali di Scienze Matematiche e Fisiche, 6, 479480


Flajolet, P. (1980) Combinatorial aspects of continued fractions. Discrete Mathematics, 32(2): 125161


Goubi, M. (2020) A new class of generalized polynomials associated with HermiteBernoulli polynomials. Journal of Applied Mathematics and Informatics, 38 (34), 211220


Goubi, M. (2018) Successive derivatives of Fibonacci type polynomials of higher order in two variables. Filomat, 32(14): 51495159


Goubi, M. (2020) An affirmative answer to two questions concerning special case of Simsek numbers and open problems. Applicable Analysis and Discrete Mathematics, 14(1): 94105


İçöz, G., Varma, S., Sucu, S. (2016) Approximation by operators including generalized Appell polynomials. Filomat, 30(2): 429440


Kargin, L. (2017) Some Formulae for Products of Geometric Polynomials with Applications. Journal of Integer Sequences, 20 (4), Article ID: 17.4.4, 15 pages


Kim, D.S., Kim, T., Kwon, H., Park, J. (2018) Two variable higherorder Fubini polynomials. Journal of the Korean Mathematical Society, 55 (4), 975986


Komatsu, T. (2020) Continued fraction expansions of the generating functions of Bernoulli and related numbers. Indagationes Mathematicae, 31(4): 695713


Mező, I. (2013/2016) Recent developments in the theory of Stirling numbers. in: Nagoshi H. [ed.] Analytic Number Theory, Distribution and Approximation of Arithmetic objects, Proceedings of, 2013, 6880


Roman, S. (1984) The Umbral Calculus. Pure and Applied Mathematics, 111


Sheffer, I.M. (1939) Some properties of polynomial sets of type zero. Duke Mathematical Journal, 5(3): 590622


Simsek, Y. (2018) Construction method for generating functions of special numbers and polynomials arising from analysis of new operators. Mathematical Methods in the Applied Sciences, 41(16): 69346954


Tanny, S.M. (1974) On some numbers related to the Bell numbers. Canadian Mathematical Bulletin, 17(5): 733738

3

Wilf, H.S. (1994) Generatingfunctionology. Academic Press, Second Edition



