Division of Power Series: Recursive and Non-Recursive Formulas

In this paper we propose a new formula to divide power series. We develop two versions of the formula: a recursive and a non-recursive one, the latter aiming to reduce the computational cost for high-order series truncation. To use the non-recursive formula we define certain fundamental sets of summation indexes. Additional non-trivial information about effects of repetition of the indexes are needed and contabilized within a coefficient.. in the formula, we explain how to calculate the coefficient.. for each summation index by constructing appropriate mappings between the fundamental sets of indexes previous defined.