A novel machine learning framework to approximate modified Bessel functions

This article presents the precise approximations for modified Bessel functions of the second kind. Building on a well-established method for function approximation, the enhanced approach, incorporating machine learning techniques, is used to approximate Bessel functions such as K 0 , K 1 , K 1/4 , I 0 , I 1 , and I 1/3 . These approximations are demonstrated to be highly effective in various applications, such as thermal average and partition function, providing a robust alternative to repeated numerical integration.