modified Hankel functions

例句：

1. 1. In the study of nonlinear dynamics, modified Hankel functions have been widely used to model complex systems.
   在非线性动力学研究中，改良汉克尔函数被广泛用来模拟复杂的系统。
2. 2. The researchers discovered that the modified Hankel functions could effectively capture theoscillation behavior of the system.
   研究人员发现改良汉克尔函数能够有效地捕捉系统的振荡行为。
3. 3. The application of modified Hankel functions in engineering has greatly improved the accuracy and efficiency of simulation models.
   改良汉克尔函数在工程中的应用大大提高了仿真模型的准确性和效率。