Transformation of formal expansions of solutions of linear differential equations in a parameter into continued <em class="a-plus-plus">RITZ</em>-fractions

Abstract

We use the apparatus of RITZ-fractions to improve the convergence of series that represent the formal solution of linear differential equations with parameter under boundary or initial conditions. We establish conditions for the existence of this solution in the case where the parameter of the equation tends to infinity. The case of a small parameter is also considered.