  Bessel functions with pure imaginary index (order) play an important role in
corpuscular optics where they govern the dynamics of charged particles in
isotrajectory quadrupoles. Recently they were found to be of great importance
in semiconductor material characterization as they are manifested in the strain
state of crystalline material. A new algorithm which can be used for the
computation of the normal and modifed Bessel functions with pure imaginary
index is proposed. The developed algorithm is very fast to compute and for
small arguments converges after a few iterations.
