Algorithm 831

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 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]. (Source: http://dl.acm.org/)

This software is also peer reviewed by journal TOMS.

Keywords for this software

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References in zbMATH (referenced in 11 articles , 1 standard article )

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  1. Pearson, John W.; Olver, Sheehan; Porter, Mason A.: Numerical methods for the computation of the confluent and Gauss hypergeometric functions (2017)
  2. Gil, Amparo; Segura, Javier; Temme, Nico M.: An improved algorithm and a Fortran 90 module for computing the conical function (P^m_-1/2+i\tau(x)) (2012)
  3. Gil, Amparo; Segura, Javier; Temme, Nico M.: Basic methods for computing special functions (2011)
  4. Avelin, Helen: Computations of Green’s function and its Fourier coefficients on Fuchsian groups (2010)
  5. Gil, Amparo; Segura, Javier; Temme, Nico M.: Computing the conical function (P^\mu_-1/2+i\tau(x)) (2009)
  6. Shi, Wei; Wong, R.: Hyperasymptotic expansions of the modified Bessel function of the third kind of purely imaginary order (2009)
  7. Ferreira, Erasmo M.; Sesma, Javier: Zeros of the Macdonald function of complex order (2008)
  8. Ashtekar, Abhay; Pawlowski, Tomasz; Singh, Parampreet; Vandersloot, Kevin: Loop quantum cosmology of (k=1) FRW models (2007)
  9. Gautschi, Walter: Numerical quadrature computation of the Macdonald function for complex orders (2005)
  10. Gil, Amparo; Segura, Javier; Temme, Nico M.: Algorithm 831: Modified Bessel functions of imaginary order and positive argument (2004)
  11. Gil, Amparo; Segura, Javier; Temme, Nico M.: Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments (2004)