Fast parallel calculation of modified Bessel function of the second kind and its derivatives

There are three main types of numerical computations for the Bessel function second kind: series expansion, continued fraction, and asymptotic expansion. In addition, they combined in appropriate domain each. However, there some regions where combination these requires sufficient computation time to achieve accuracy, however, efficiency is significantly reduced when parallelized. proposed method, we adopt a simple integration concept integral representation. We coarsely refine range beforehand, stabilize by performing calculation at fixed number intervals. Experiments demonstrate that method can same level accuracy as existing methods less than half time.