On the construction of solutions of systems of linear ordinary differential equations in the neighbourhood of a regular singularity

AbstractA method allowing to construct successively all linearly independent solutions of systems of linear ordinary differential equations in the neighbourhood of a regular singularity as algebraic combinations of a power series, power and a logarithmic function log x is proposed. The solutions are constructed both in the cases of a simple and defect “leading” matrix of coefficients in equations. The convergence of power series in solutions is proven and the estimate of the errors which arise due to the truncation of these series is obtained. An application of the method to solving one-particle Schrödinger equations is discussed