numerical-methodsbessel-functions

Algorithm to calculate modified Bessel function of the first kind

Could you tell me a fast and accurate method to calcuate BesselK(mu,z), BesselI(mu,z), where mu is real number?

Solution

  • There are several ways to represent the Bessel functions and none of them are easy to do mathematically or closed-form. However, this paper seems to be a recent approach to evaluating them efficiently:

    http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.120.6055

    It seems to be a better way than the old-school method from the 1950s:

    http://www.ams.org/journals/mcom/1959-13-066/S0025-5718-1959-0105794-5/S0025-5718-1959-0105794-5.pdf