Efficient Multi-Precision Computation of Bessel Functions for Real Orders and Complex Arguments with a Fortran Implementation -- Part III: Regular Bessel Functi... (opens in new tab)

This paper is the final part in a series devoted to the development of numerically stable and efficient algorithms, together with multi-precision Fortran implementations, for computing Bessel functions with real orders and complex arguments. Parts~I and~II presented stable and efficient algorithms for the modified Bessel functions I_nu(z) and K_nu(z); here we treat Bessel functions J_nu(z) and Y_nu(z). The proposed algorithms support complex arg...