On linear equations with general polynomial solutions

On Generalized Solutions of Locally Fuchsian Ordinary Differential Equations

“…Studies on the existence of polynomial solutions has been carried out by say [2] where the authors propose a new approach for investigating polynomial solutions based on elementary linear algebra. Laradji [14] considers a general n-th order linear ODE and provides the necessary and sufficient conditions for which it has a general polynomial solution. For the special case of Fuchsian ordinary differential equations the classical functions exist in general [3].…”