Algorithm 831: Modified Bessel functions of imaginary order and positive argument

  • Authors:

  • Amparo Gil;Javier Segura;Nico M. Temme

  • Affiliations:

  • U. Autónoma de Madrid, Santander, Spain;U. de Cantabria, Santander, Spain;CWI, Amsterdam, The Netherlands

  • Venue:
  • ACM Transactions on Mathematical Software (TOMS)
  • Year:
  • 2004

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Abstract

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 x2w" + xw' + (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].