We give a complete expansion, at any accuracy order, for the iterated convolution of a complex valued integrable sequence in one space dimension. The remainders are estimated sharply with generalized Gaussian bounds. The result applies in probability theory for random walks as well as in numerical analysis for studying the large time behavior of numerical schemes.

翻译：本文针对一维空间中的复数值可积序列，给出了其迭代卷积在任意精度阶下的完整展开。余项通过广义高斯界进行锐利估计。该结果在概率论中适用于随机游走的研究，同时在数值分析中可用于探讨数值格式的大时间行为。