TY - INPR A1 - Stiefenhofer, Matthias T1 - A note on an expansion formula with application to nonlinear Differential-Algebraic-Equations N2 - In [DL] systems of differential polynomials are investigated with respect to properties of Artin approximation type. The key tool in [DL] is an extended version of a formula by Hurwitz [Hu] expressing high order derivatives of an expansion by lower ones. The formula is further refined in [VFZ] to deliver sufficient conditions concerning the existence of power series solutions of scalar algebraic differential equations of order?. In the paper at hand, the main results from [VFZ] are first reproduced and further extended to systems of nonlinear differential algebraic equations. In addition, a simple extension of Tougeron’s implicit function theorem is given in a specific constellation. The results follow from [S1], [S2] where Artin approximation is treated within a Banach space setting, thereby constructing an expansion formula that expresses accurately the required dependency of low and high order derivatives within the system of undetermined coefficients. KW - AlgGeo KW - Differential polynomials KW - Hurwitz expansion formula KW - Separant matrix Y1 - 2019 UR - https://opus4.kobv.de/opus4-hs-kempten/frontdoor/index/index/docId/581 UR - https://nbn-resolving.org/urn:nbn:de:bvb:859-5812 CY - Kempten ER -