Formal Power Series and Linear Systems of Meromorphic Ordinary Differentialequations

Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a formal solution of a certain form, which can be relatively easily computed, but which generally involves such power series diverging everywhere. In this book the author presents the classical theory of meromorphic systems of ODE in the new light shed upon it by the recent achievements in the theory of summability of formal power series.Balser, Werner is the author of 'Formal Power Series and Linear Systems of Meromorphic Ordinary Differentialequations' with ISBN 9780387986906 and ISBN 0387986901.