Bell polynomials and generalized Laplace transforms

An extension of the Laplace transform obtained by using the Laguerre-type exponentials is first shown. Furthermore, the solution of the Blissard problem by means of the Bell polynomials, gives the possibility to associate to any numerical sequence a Laplace-type transform depending on that sequence. Computational techniques for the corresponding transform of analytic functions, involving Bell polynomials, are derived. AMS 2010 Mathematics Subject Classifications: 44A10, 05A40, 11B83.

[1]  Francesco Faà di Bruno.  Théorie des formes binaires , 1876 .

[2]  On a generalized three-parameter wright function of Le Roy type , 2017, 2007.05925.

[3]  E. C. Titchmarsh,et al.  The Laplace Transform , 1991, Heat Transfer 1.

[4]  P. Ricci,et al.  An introduction to operational techniques and special polynomials , 2009 .

[5]  Paolo Ricci,et al.  Bell polynomials and differential equations of Freud-type polynomials , 2002 .

[6]  A. D. Bucchianico.  Probabilistic and analytical aspects of the umbral calculus , 1997 .

[7]  John Riordan,et al.  Introduction to Combinatorial Analysis , 1959 .

[8]  Clemente Cesarano,et al.  Laguerre-type exponentials and generalized Appell polynomials , 2004 .

[9]  Dongkyu Lim,et al.  Some properties and an application of multivariate exponential polynomials , 2020, Mathematical Methods in the Applied Sciences.

[10]  C. Cesarano,et al.  Laguerre-type bessel functions , 2005 .

[11]  Silvia Noschese,et al.  Differentiation of Multivariable Composite Functions and Bell Polynomials , 2003 .

[12]  Pierpaolo Natalini,et al.  Higher order Bell polynomials and the relevant integer sequences , 2017 .

[13]  G. Maroscia,et al.  Laguerre-type BVP and generalized Laguerre polynomials , 2006 .

[14]  Tianming Wang,et al.  Identities on Bell polynomials and Sheffer sequences , 2009, Discret. Math..

[15]  Paolo Emilio Ricci,et al.  Laguerre-type special functions and population dynamics , 2007, Appl. Math. Comput..

[16]  Giuseppe Dattoli,et al.  Eigenfunctions of laguerre-type operators and generalized evolution problems , 2005, Math. Comput. Model..

[17]  Pierpaolo Natalini,et al.  An extension of the bell polynomials , 2004 .

[18]  Aldo Ghizzetti,et al.  Trasformate di Laplace e calcolo simbolico , 1971 .

[19]  Paolo Emilio Ricci,et al.  Bell polynomials and modified Bessel functions of half-integral order , 2015, Appl. Math. Comput..

[20]  Pierpaolo Natalini,et al.  Multidimensional bell polynomials of higher order , 2005 .

[21]  Paolo Emilio Ricci,et al.  Modelling population growth vialaguerre-type exponentials , 2005, Math. Comput. Model..

[22]  Joel Anderson.  Iterated Exponentials , 2004, Am. Math. Mon..

[23]  Giuseppe Dattoli,et al.  Laguerre-Type Exponentials, and the Relevant 𝐿-Circular and 𝐿-Hyperbolic Functions , 2003 .

[24]  Federico Polito,et al.  On some operators involving Hadamard derivatives , 2013, 1304.1058.

[25]  Mourad E. H. Ismail,et al.  A -umbral calculus , 1981 .

[26]  R. Corcino,et al.  On Generalized Bell Polynomials , 2011 .

[27]  Feng Qi (祁锋),et al.  Special values of the Bell polynomials of the second kind for some sequences and functions , 2020, Journal of Mathematical Analysis and Applications.

[28]  L. Comtet,et al.  Advanced Combinatorics: The Art of Finite and Infinite Expansions , 1974 .