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On similarities between exponential polynomials and hermite polynomials

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The aim of this paper is to introduce and compare some fundamental analytical properties of the title polynomials. Many similarities between them are emphasized in the paper. Moreover, the authors present many isolated results, new proofs and identities.
Rocznik
Strony
93--104
Opis fizyczny
Bibliogr. 27 poz.
Twórcy
autor
  • Institute of Mathematics, Silesian University of Technology Gliwice, Poland
  • Institute of Mathematics, Silesian University of Technology Gliwice, Poland
autor
  • Institute of Mathematics, Silesian University of Technology Gliwice, Poland
autor
  • Institute of Mathematics, Silesian University of Technology Gliwice, Poland
Bibliografia
  • [1] Bell E.T., Exponential polynomials, Ann. Math. 1934, 35(2), 258-277.
  • [2] Nadarajah S., Simple formulas for certain polynomials, Appl. Math. Comput. 2007, 187, 1592-1596.
  • [3] Ehrenborg R., The Hankel determinant of exponential polynomials, Amer. Math. Monthly 2000, 107, 557-560.
  • [4] Graham R.L., Knuth D.E., Patashnik O., Concrete Mathematics, Addison-Wesley, Reading 1994.
  • [5] Knuth D.E., Stirling numbers, Amer. Math. Monthly 1995, 102, 562.
  • [6] Gould H.W., Quaintance J., A linear binomial recurrence and the Bell numbers and polynomials, Appl. Anal. Discrete Math. 2007, 1, 371-385.
  • [7] Comtet L., Advanced Combinatorics, D. Riedel, Dordrecht 1974.
  • [8] Lukacs E., Characteristic Functions, Hafner Publishing Co., New York 1970.
  • [9] Di Bucchianico A., Loeb D., A selected survey of umbral calculus, Electron. J. Combin., Dynamic Surveys 2000, DS3.
  • [10] Gessel I.M., Applications of the classical umbral calculus, Algebra Universalis 2003, 49, 397-434.
  • [11] Roman S.M., Rota G.C., The umbral calculus, Advances in Math. 1978, 27, 95-188.
  • [12] Radoux Ch., The Henkel determinant of exponential polynomials: a very short proof a new result concerning Euler numbers, Amer. Math. Monthly 2002, 109, 277-278.
  • [13] Gould H.W., Quaintance J., Implications of Spivey's Bell number formula, J. Integer Sequences 2008, 11, Article 08.3.7.
  • [14] Fekete A., Cigler J., Stirling and Bell and binomial, Oh my! Amer. Math. Monthly 2002, 109, 476-477.
  • [15] El-Mikkawy M., A note on the reducibility of special infinite series, Appl. Math. Comput. 2005, 162, 311-315.
  • [16] Harper L.H., Stirling behavior is asymptotically normal, Ann. Math. Stat. 1967, 38, 401-414.
  • [17] Brillhart J., Note on the single variable Bell polynomials. Amer. Math. Monthly 1967, 74, 695-696.
  • [18] Cakić N.P., On some combinatorial identities, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 1980, 678-715, 91-94.
  • [19] Cakić N.P., On the numbers related to the Stirling numbers of the second kind, Facta Univ. Ser. Math. Inform. 2007, 22 , 105-108.
  • [20] Suetin P.K., Classical Orthogonal Polynomials, Nauka, Moscow 1976 (in Russian).
  • [21] Ma S.-M., Wang Y., q-Eulerian polynomials and polynomials with only real zeros, Electron. J. Combin. 2008, 15, #R17.
  • [22] Liu L., Wang Y., A unified approach to polynomial sequences with only real zeros, Adv.in Appl. Math. 2007, 38, 542-560.
  • [23] Olver F.W.J., Lozier D.W., Boisvert R.F., Clark C.W. (eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, Cambridge 2010.
  • [24] Dorwart H.L., Irreducibility of polynomials, Amer. Math. Monthly 1935, 42, 369-381.
  • [25] Kalinowski M.W., Seweryński M., Differential equation for Hermite-Bell polynomials, Math. Proc. Phil. Soc. 1982, 91(2), 259-265.
  • [26] Dominici D., Asymptotic analysis of generalized Hermite polynomials, Analysis 2008, 28, 239-261.
  • [27] Paris R.B., The asymptotics of the generalized Hermite-Bell polynomials, J. Comp. Appl. Math. 2009, 232, 216-226.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-5367e553-83dd-42cc-ad03-3017dff0a7a1
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