Regular Solutions of Linear Ordinary Differential Equations and Truncated Series

Abstract

Abstract: Linear ordinary differential equations with coefficients in the form of truncated formal power series are considered. Earlier, it was discussed what can be found from an equation specified in this way about its solutions belonging to the field of formal Laurent series. Now a similar question is discussed for regular solutions. We are still interested in information about these solutions that is invariant under possible prolongations of truncated series representing the coefficients of the equation. The possibility of including in the solutions symbolic unspecified coefficients of possible prolongations of the equation is also considered.