标题： 解析评估多重梅林-巴恩斯积分 显示英文标题

标题： Analytic Evaluation of Multiple Mellin-Barnes Integrals

摘要： 我们总结了两种几何方法来解析评估高重 Mellin-Barnes (MB) 积分，并将其表示为超几何函数。第一种方法基于锥包的交集，而第二种方法（较近期）则依赖于点集的三角剖分。我们证明，一旦实现自动化，三角剖分方法在计算上比锥包方法更高效。作为这种三角剖分方法的应用，我们描述了如何从之前通过锥包方法得到的结果中，导出共形非闭壳无质量两圈双盒和一阶六边形费曼积分的更简单的超几何解。最后，通过对多重多对数 MB 表达式的上述技术应用，我们展示了如何获得这些函数的新收敛级数表示形式。这些新的解析表达式已用 GINAC 进行了数值交叉验证。 显示英文摘要

摘要： We summarize two geometrical approaches to analytically evaluate higher-fold Mellin-Barnes (MB) integrals in terms of hypergeometric functions. The first method is based on intersections of conic hulls, while the second one, which is more recent, relies on triangulations of a set of points. We demonstrate that, once automatized, the triangulation approach is computationally more efficient than the conic hull approach. As an application of this triangulation approach, we describe how one can derive simpler hypergeometric solutions of the conformal off-shell massless two-loop double box and one-loop hexagon Feynman integrals than those previously obtained from the conic hull approach. Lastly, by applying the above techniques on the MB representation of multiple polylogarithms, we show how to obtain new convergent series representations for these functions. These new analytic expressions were numerically cross-checked with GINAC.