Schimming, Rainer; Rida, Saad Zagloul Noncommutative Bell polynomials. (English) Zbl 0899.33006 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) Cited in 2 ReviewsCited in 12 Documents 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 PDF BibTeX XML Cite \textit{R. Schimming} and \textit{S. Z. Rida}, Int. J. Algebra Comput. 6, No. 5, 635--644 (1996; Zbl 0899.33006) Full Text: DOI