Nonlinear transformation of series. II
The paper is closely related to a previous paper of the authors [Appl. Math. Lett. 4, No. 4, 69-71 (1991; Zbl 0742.40004)]. For \(u=\sum_{n=0}^ \infty c_ n x^ n\) the authors give in the paper cited above an analytic function \(f(u)\) which can be expressed in the form \(f(u)=\sum_{n=0}^ \infty A_ n(u_ 0,\dots,u_ n)\), where \(A_ n\) are so called Adomian polynomials. This procedure is extended here for functions of several variables. Some applications in the theory of ordinary differential equations are given.
scientific article; zbMATH DE number 60651