The method for obtaining expressions for coefficients of reverse generating functions

Abstract

The powers of generating functions and its properties are analyzed. A new class of functions is introduced, based on the application of compositions of an integer $n$, called composita. The methods for obtaining reciprocal and reverse generating functions, and solutions of the functional equations $F(A(x))=G(x)$, where $A(x)$ is an unknown generating function, are proposed. Key words: generating functions, reverse, reciprocal, composita, method.