Fast Calculation of the Derivatives of Bessel Functions with Respect to the Parameter and Applications

In this paper, the fast algorithms of the derivatives of Bessel functions with respect to the parameter are obtained. Based on these fast algorithms, we discuss the calculations of the derivatives of the functions related to the heterogeneous Bessel differential equation, such as Anger, Weber, Struve and modified Struve functions. In addition, the fast calculation of some integrals related to these functions are obtained. At last, numerical examples show the algorithms given in this paper are fast and high precision.