We develop some extensions of the classical Bell polynomials, previously obtained, by introducing a further class of these polynomials called multidimensional Bell polynomials of higher order. They arise considering the derivatives of functions f in several variables φ(i), (i = 1, 2, …, m), where φ(i) are composite functions of different orders, i.e. φ(i) (t) = (i,1) ((i,2) (… ((i,ri) (t))), (i = 1, 2, …, m). We show that these new polynomials are always expressible in terms of the ordinary Bell polynomials, by means of suitable recurrence relations or formal multinomial expansions. Moreover, we give a recurrence relation for their computation.
A. BERNARDINI, NATALINI P, & P.E. RICCI (2005). Multi-dimensional Bell polinomials of higher order. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 50, 1697-1708 [10.1016/j.camwa.2005.05.008].
Titolo: | Multi-dimensional Bell polinomials of higher order | |
Autori: | ||
Data di pubblicazione: | 2005 | |
Rivista: | ||
Citazione: | A. BERNARDINI, NATALINI P, & P.E. RICCI (2005). Multi-dimensional Bell polinomials of higher order. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 50, 1697-1708 [10.1016/j.camwa.2005.05.008]. | |
Abstract: | We develop some extensions of the classical Bell polynomials, previously obtained, by introducing a further class of these polynomials called multidimensional Bell polynomials of higher order. They arise considering the derivatives of functions f in several variables φ(i), (i = 1, 2, …, m), where φ(i) are composite functions of different orders, i.e. φ(i) (t) = (i,1) ((i,2) (… ((i,ri) (t))), (i = 1, 2, …, m). We show that these new polynomials are always expressible in terms of the ordinary Bell polynomials, by means of suitable recurrence relations or formal multinomial expansions. Moreover, we give a recurrence relation for their computation. | |
Handle: | http://hdl.handle.net/11590/151083 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |