A variant of van Hoeij's algorithm to compute hypergeometric term solutions of holonomic recurrence equations

Linear and homogeneous recurrence equations having poly-nomial coefficients are said to be holonomic. These equa-tions are useful for proving and discovering combinatorial and hypergeometric identities. Given a field K of charac-teristic zero, an is a hypergeometric term with respect to K, if the ratio an+1/an is a rational function over K. Two al-gorithms by Marko Petkovˇsek (1993) and Mark van Hoeij (1999) were proposed to compute hypergeometric term so-lutions of holonomic recurrence equations. The latter algo-rithm is more efficient and was implemented by its author in the Computer Algebra System (CAS) Maple through the command LREtools[hypergeomsols]. We describe an equally efficient algorithm that ignores some recommen-dations of van Hoeij’s approach.