This paper continues the studies of symbolic integration by focusing on the stability problems on D-finite functions. We introduce the notion of stability index in order to investigate the order growth of the differential operators satisfied by iterated integrals of D-finite functions and determine bounds and exact formula for stability indices of several special classes of differential operators. With the basic properties of stability index, we completely solve the stability problem on general hyperexponential functions.

翻译：本文延续符号积分的研究，聚焦于D-有限函数的稳定性问题。我们引入稳定性指数的概念，以探究D-有限函数的迭代积分所满足的微分算子阶数增长规律，并确定了若干特殊微分算子类的稳定性指数边界及精确公式。借助稳定性指数的基本性质，我们完整解决了广义超指数函数的稳定性问题。