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Algorithm 831: Modified Bessel functions of imaginary order and positive argument. (English) Zbl 1072.65025
Summary: 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)(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].
MSC:
65D20Computation of special functions, construction of tables
33C10Bessel and Airy functions, cylinder functions, 0 F 1
33F05Numerical approximation and evaluation of special functions
65Y15Packaged methods in numerical analysis
Software:
Algorithm 831; AIZ; BIZ