Ordinary Bessel functions are a common function used when examining the spectral properties of frequency modulated signals, particularly in sound synthesis applications. Recently, it was shown that modified Bessel functions can also be used for sound synthesis. However, to limit the impact of aliasing distortion when using these functions, it is essential to set an upper limit on the frequency-dependent modulation index used when computing these functions. However, it can be impossible to do this beyond a certain threshold when using standard mathematical software tools such as Matlab, or the scientific toolbox of the Python language, because of numerical overflow issues. This short paper presents an approach to overcome this limitation using the MaxStar algorithm. Results are also presented to demonstrate the usefulness of this solution.