Symbolic solution of nonhomogeneous linear ordinary differential equations in terms of power series

Abstract

For a nonhomogeneous linear ordinary differential equation Ly(x) = f(x) with polynomial coefficients and a holonomic right-hand side, a set of points x = a is found where a power series solution $$y(x) = \sum\nolimits_{n = 0}^\infty {c_n (x - a)} ^n $$ with hypergeometric coefficients exists (starting from some number, the ratio c n + 1/c n is a rational function of n).