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On the sequences of polynomials and their generating functions. (English) Zbl 07801861

Summary: We give first of all, an identity having interesting applications on polynomials and some combinatorial sequences. Secondly, we refer two interesting formulas on generating functions of polynomials. Our results are illustrated by some comprehensive examples.

MSC:

05A15 Exact enumeration problems, generating functions
11B83 Special sequences and polynomials

References:

[1] P. Appell, Sur une classe de polynômes, Ann. Sci. Ecole Norm. Sup. 9 (1880), 119-144. · JFM 12.0342.02
[2] A.Z. Broder, The r-Stirling numbers, Discrete Math., 49, 241-259, (1984). · Zbl 0535.05006
[3] J.W. Brown, New generating functions for classical polynomials, Proc. Amer. Math. Soc., 21, 263-268, (1969). · Zbl 0175.07302
[4] J.D.E. Konhauser, Biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math. 21, 303-314, (1967). · Zbl 0156.07401
[5] M.S. Maamra and M. Mihoubi, The (r 1 , . . . , rp)-Bell polynomials, Integers, 14, #A34, (2014). · Zbl 1308.11027
[6] Z.A. Melzak, V.D. Gokhale, and W.V. Parker, Advanced problems and solutions: 4458, Amer. Math. Monthly, 60 (1), 53-54, (1953).
[7] Z.A. Melzak, D.J. Newman, P. Erdös, G. Grossman, and M.R. Spiegel, Advanced problems and solutions: 4458, Amer. Math. Monthly, 58 (9), p. 636, (1951).
[8] I. Mező, On the maximum of r-Stirling numbers, Adv. Appl. Math., 41, 293-306, (2008). · Zbl 1165.11023
[9] M. Mihoubi, Bell polynomials and binomial type sequences. Discrete Math. 308, 2450-2459, (2008). · Zbl 1147.05006
[10] M. Mihoubi and M. Sahari, On some polynomials applied to the theory of hyperbolic differential equations, Submitted. · Zbl 1465.11073
[11] M. Mihoubi and M. Sahari, On a class of polynomials connected to Bell polynomials, Arxiv (2018), avalaible at http://arxiv.org/abs/1801.01588v2
[12] J. Riordan, Combinatorial Identities, John Wiley, New York, (1968). · Zbl 0194.00502
[13] H.M. Sristava and J.P. Singhal, New generating functions for Jacobi and related polynomials, J. Math. Anal. Appl., 41 (1973), pp. 748-752. · Zbl 0218.33006
[14] K.R. Stromberg, Introduction to classical real analysis, Wadsworth, (1981). · Zbl 0454.26001
[15] H.S. Wilf, generatingfunctionology, 2nd edition. Academic Press, San Diego, (1994). · Zbl 0831.05001
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