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Noncommutative Bell polynomials. (English) Zbl 0899.33006
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.

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