Numerical Evaluation of Spherical Bessel and Related Functions

Abstract

Techniques for calculating the spherical Bessel functions of complex argument lying in any quadrant of the z-plane and arbitary orders have been developed. The method applies to real, pure imaginary or complex arguments. Sample results are given for a range of arguments and for selected orders ranging from 0 to 200. It has been found that these functions for various quadrants are interrelated. We have noticed the following unusual result: provided that Im z is large compared to unity and Re z is too near zero, the functions Jn + 1/2 (z) and Yn + 1/2 (z) are interdependent in the sense that one can be derived from the other upto a certain maximum order n. Furthermore, if z lies on postive or negative y-axis, it has been found that the corresponding Bassel functions satisfy certain special properties.