Algorithm 831: Modified Bessel functions of imaginary order and positive argument
Fortran 77 programs for the computation of modified Bessel functions of purely imaginary order are presented. The codes compute the functions K-ia(x), L-ia(x) and their derivatives for real a and positive x; these functions are independent solutions of the differential equation x(2)w" + xw' + (a(2-)x(2))w = 0. The code also computes exponentially scaled functions. The range of computation is (x,a) is an element of (0, 1500] x [-1500, 1500] when scaled functions are considered and it is larger than (0, 500] x [-400, 400] for standard IEEE double precision arithmetic. The relative accuracy is better than 10(-13) in the range (0, 200] x[-200, 200] and close to 10(-12) in (0, 1500] x[-1500, 1500].
algorithms bessel functions numerical quadrature asymptotic expansions