International Journal of Algebra and Computation · 1996 · 31 citations · 0 references
Natural SciencesMathematicsPhysicsAlgebraDifferential EquationsDynamical SystemsBellman EquationsIntegral EquationsNoncommutative AlgebraOperator Theory
The recursive definition for the sequence of the Bell polynomials is generalized to noncommutative variables and then explicitly solved. As applications, we 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.