Symbolic Conversion of Holonomic Functions to Hypergeometric Type Power Series

A term an is m-fold hypergeometric, for a given positive integer m, if the ratio $${{a}_{{n + m}}}{\text{/}}{{a}_{n}}$$ rational function over field $$\mathbb{K}$$ of characteristic zero. We establish structure holonomic recurrence equations, i.e. linear and homogeneous equations having polynomial coefficients, that have hypergeometric solutions , any m. Consequently, we describe new algorithm, say mfoldHyper, extends algorithms by Petkovšek (1992) van Hoeij (1998) which compute basis (m = 1) to more general case terms.