Algorithm xxx: Modified Bessel functions of imaginary order and positive argument
<|reference_start|>Algorithm xxx: 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 $x^2 w'' +x w' +(a^2 -x^2)w=0$. The code also computes exponentially scaled functions. The range of computation is $(x,a)\in (0,1500]\times [-1500,1500]$ when scaled functions are considered and it is larger than $(0,500]\times [-400,400]$ for standard IEEE double precision arithmetic. The relative accuracy is better than $10^{-13}$ in the range $(0,200]\times [-200,200]$ and close to $10^{-12}$ in $(0,1500]\times [-1500,1500]$.<|reference_end|>
@article{gil2004algorithm,
    title={Algorithm xxx: Modified Bessel functions of imaginary order and positive
  argument},
    author={Amparo Gil, Javier Segura, Nico M. Temme},
    journal={arXiv preprint arXiv:cs/0401008},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0401008},
    primaryClass={cs.MS cs.NA math.NA}
}