On expansion of algebraic functions in power and Puiseux series, II
David V. Chudnovsky, Gregory V. Chudnovsky · Journal of Complexity · 1987
We present algorithms that determine coefficients in the expansions of solutions of linear differential equations in the neighborhood of regular singularities using explicit linear recurrences. These algorithms combined with Newton's method allow one to compute the Nth coefficient (or N coefficients) of an algebraic function of degree d in O(dN) operations with O(d) storage (or O(dN) storage).