Generation of bessel functions with complex arguments and integer orders

Abstract

Algorithms have been presented for generating the Bessel functions J ⁿ (z)Y ⁿ (z) and their derivatives, where z is complex and n an integer. The values of the functions generated by the proposed method are accurate to almost as many significant places as are available on the computer. Also, the ranges of n and z for which the functions can be generated to this accuracy are limited only by the overflow and underflow limits of the machine. The methods and the numerical aspects of the problem have been discussed in detail. The computed results of the functions for real and complex arguments have been checked against standard tables wherever possible. Some sample tables for specific values of n and z have also been presented.

Keywords:

• Bessel functions
• Gaussian integration method
• bisection method

C.R. Categories:

• I.1.2