Algorithm xxx: Modified Bessel functions of imaginary order and positive argument

Original · EN

Fortran 77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions Kia(x), Lia(x) and their derivatives for real a and positive x; these functions are independent solutions of the differential equation x² w'' +x w' +(a² -x²)w=0. The code also computes exponentially scaled functions. The range of computation is (x,a)∈ (0,1500]× [-1500,1500] when scaled functions are considered and it is larger than (0,500]× [-400,400] for standard IEEE double precision arithmetic. The relative accuracy is better than 10⁻¹³ in the range (0,200]× [-200,200] and close to 10⁻¹² in (0,1500]× [-1500,1500].