Noncommutative Bell polynomials. (English) Zbl 0899.33006

Schimming, Rainer; Rida, Saad Zagloul

Int. J. Algebra Comput. 6, No. 5, 635-644 (1996).

The recursive definition for the sequence of the Bell polynomials is generalized to non-commutative variables and then explicitly solved. As applications, the authors present formulas for the powers of a first-order matrix-valued differential operator, of the “substantial derivative” to a dynamical system, and for the Taylor coefficients of the time-ordered exponential integral.

Reviewer: R.Schimming (Greifswald)

MSC:

33C45	Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
11B83	Special sequences and polynomials
39A10	Additive difference equations

Keywords:

Bell polynomials; non-commutative variables; Taylor coefficients