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., B., Natalini, P., P. E., R. (2005). Multi-dimensional Bell polinomials of higher order. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 50, 1697-1708 [10.1016/j.camwa.2005.05.008].
Multi-dimensional Bell polinomials of higher order
NATALINI, PIERPAOLO;
2005-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
