We present efficient methods for calculating linear recurrences of hypergeometric double sums and, more generally, of multiple sums. In particular, we supplement this approach with the algorithmic theory of contiguous relations, which guarantees the applicability of our method for many input sums. In addition, we elaborate new techniques to optimize the underlying key task of our method to compute rational solutions of parameterized linear recurrences.

翻译：本文提出了计算超几何型双重和（以及更一般地，多重和）线性递推关系的高效方法。特别地，我们通过相邻关系的算法理论对该方法进行了补充，从而保证了该方法对众多输入求和的适用性。此外，我们开发了新的技术手段来优化该方法中计算参数化线性递归有理解这一核心任务。