136
Views
2
CrossRef citations to date
0
Altmetric
Research Articles

Bell polynomials and generalized Laplace transforms

Pages 966-977 | Received 11 Mar 2022, Accepted 24 Mar 2022, Published online: 05 Apr 2022

References

  • Ghizzetti A, Ossicini A. Trasformate di Laplace e calcolo simbolico (Italian). Torino: UTET; 1971.
  • Widder DV. The Laplace transform. New York: Princeton University Press; 1946.
  • Bell ET. Exponential polynomials. Ann Math. 1934;35:258–277.
  • Bernardini A, Ricci PE. Bell polynomials and differential equations of Freud-type polynomials. Math Comput Model. 2002;36:1115–1119.
  • Cassisa C, Ricci PE. Orthogonal invariants and the Bell polynomials. Rend Mat Appl. 2000;20:293–303.
  • Di Cave A, Ricci PE. Sui polinomi di Bell ed i numeri di Fibonacci e di Bernoulli. Le Matematiche. 1980;35:84–95.
  • Natalini P, Ricci PE. Bell polynomials and modified Bessel functions of half-integral order. Appl Math Comput. 2015;268:270–274.
  • Fujiwara D. Generalized Bell polynomials. Sūgaku. 1990;42:89–90.
  • Rai PN, Singh SN. Generalization of Bell polynomials and related operatorial formula. (Hindi). Vijnana Parishad Anusandhan Patrika. 1982;25:251–258.
  • Bernardini A, Natalini P, Ricci PE. Multi-dimensional Bell polynomials of higher order. Comput Math Appl. 2005;50:1697–1708.
  • Natalini P, Ricci PE. An extension of the Bell polynomials. Comput Math Appl. 2004;47:719–725.
  • Noschese S, Ricci PE. Differentiation of multivariable composite functions and Bell Polynomials. J Comput Anal Appl. 2003;5:333–340.
  • Qi F, Da-Wei N, Dongkyu L, et al. Some properties and an application of multivariate exponential polynomials. Math Methods Appl Sci. 2020;43(6):2967–2983.
  • Natalini P, Ricci PE. Higher order Bell polynomials and the relevant integer sequences. Appl Anal Discrete Math. 2017;11:327–339. DOI:10.2298/AADM1702327N
  • Qi F, Niu D-W, Lim D, et al. Special values of the Bell polynomials of the second kind for some sequences and functions. J Math Anal Appl. 2020;491(2):Article ID 124382.
  • Wang W, Wang T. Identities on Bell polynomials and Sheffer sequences. Discrete Math. 2009;309:1637–1648.
  • Riordan J. An introduction to combinatorial analysis. Chichester: Wiley; 1958.
  • Faà di Bruno F. Théorie des formes binaires. Turin: Brero; 1876.
  • Roman SM, Rota GC. The umbral calculus. Adv Math. 1978;27:95–188.
  • Roman SM. The umbral calculus. New York (NY): Academic Press; 1984.
  • Comtet L. Advanced combinatorics: the art of finite and infinite expansions. D. Reidel Publishing Co.; 1974. DOI:10.1007/978-94-010-2196-8
  • Kim T, Kim DS, Jang L-C, et al. Complete and incomplete Bell polynomials associated with Lah-Bell numbers and polynomials. Adv Differ Equ. 2021;2021:Paper No. 101, 12 pp.
  • Kwon J, Kim T, Kim DS, et al. Some identities for degenerate complete and incomplete r-Bell polynomials. J Inequal Appl. 2020;2020Paper No. 23, 9 pp.
  • Blissard J. Theory of generic functions. Quart J Pure Appl Math. 1861;4:279–305. 1862;5:58–75, 185–208.
  • Di Bucchianico A. Probabilistic and analytical aspects of the umbral calculus. Amsterdam: Stichting Math. Centrum; 1997.
  • Dattoli G, Ricci PE. Laguerre-type exponentials, and the relevant L-circular and L-hyperbolic functions. Georgian Math J. 2003;10:481–494.
  • Le Roy È. Valeurs asymptotiques de certaines séries procédant suivant les puissances entières et positives d'une variable réelle (French). Darboux Bull (2). 1899;4:245–268.
  • Garra R, Polito F. On some operators involving Hadamard derivatives. Integral Transforms Spec Funct. 2013;24(10):773–782.
  • Garrappa R, Rogosin S, Mainardi F. On a generalized three-parameter Wright function of Le Roy type. Fract Calc Appl Anal. 2017;20(5):1196–1215. DOI:10.1515/fca-2017-0063
  • Ricci PE, Tavkhelidze I. An introduction to operational techniques and special polynomials. J Math Sci. 2009;157:161–189.
  • Bernardini A, Dattoli G, Ricci PE. L-exponentials and higher order Laguerre polynomials. In: Proceedings of the Fourth International Conference of the Society for Special Functions and their Applications (SSFA). Chennai: Soc. Spec. Funct. Appl.; 2003. p. 13–26.
  • Bernardini A, Bretti G, Ricci PE. Laguerre-type exponentials, multidimensional special polynomials and applications. Lecture Notes TICMI. 2004;5:1–28.
  • Bretti G, Cesarano C, Ricci PE. Laguerre-type exponentials and generalized Appell polynomials. Comput Math Appl. 2004;48:833–839.
  • Cesarano C, Germano B, Ricci PE. Laguerre-type Bessel functions. Integral Transforms Spec Funct. 2005;16:315–322.
  • Bretti G, Ricci PE. Laguerre-type special functions and population dynamics. Appl Math Comp. 2007;187:89–100.
  • Dattoli G, He MX, Ricci PE. Eigenfunctions of Laguerre-type operators and generalized evolution problems. Math Comput Model. 2005;42:1263–1268.
  • De Andreis S, Ricci PE. Modelling population growth via Laguerre-type exponentials. Math Comput Model. 2005;42:1421–1428.
  • Maroscia G, Ricci PE. Laguerre-type BVP and generalized Laguerre polynomials. Integral Transforms Spec Funct. 2006;17:577–590.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.