Difference equations (i.e. recurrence equations) have a number of properties in common with differential equations. The PI recently introduced the notion of finite singularities of difference equations. With this notion, more methods for differential equations can now be applied to difference equations, and this leads to new algorithms. In particular, the PI intends to implement a new efficient algorithm for computing hypergeometric solutions of recurrence equations. These algorithms have several applications, such as finding and proving formulas, or solving certain linear differential equations.
