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

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.

Automated summary

Bell's polynomials can be used to approximate the Laplace Transform of composite functions and higher-order nested functions. The article introduces an extension of Bell's polynomials for representing the derivatives of multiple nested functions. Worked examples are provided, and the polynomials used are reported in the appendices.