Bell’s Polynomials and Laplace Transform of Higher Order Nested Functions

Abstract

Using Bell’s polynomials it is possible to approximate the Laplace Transform of composite functions. The same methodology can be adopted for the evaluation of the Laplace Transform of higher-order nested functions. In this case, a suitable extension of Bell’s polynomials, as previously introduced in the scientific literature, is used, namely higher order Bell’s polynomials used in the representation of the derivatives of multiple nested functions. Some worked examples are shown, and some of the polynomials used are reported in the Appendices.