Algorithms for Solving Linear Recurrence Equations

Van HoeijDifference方程(即递归方程)与微分方程有许多共同的性质。PI最近引入了差分方程组的有限奇点的概念。有了这个概念，现在可以将更多的微分方程组方法应用到差分方程组中，这就产生了新的算法。特别是，PI旨在实现一种新的高效算法来计算递归方程的超几何解。这些算法有几个应用，如寻找和证明公式，或求解某些线性微分方程组。

9805983van HoeijDifference 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.