Numerical Evaluation of Bessel Functions of First, Second and Third Kind of Complex Argument and Integer Orders

摘要

The double precision of the Bessel functions of integer orders in the entire complex plane is discussed. The Hankel asymptotic expansions are used. Significant digits are lost in solution of Bessel's equation due to essential singularity at zero or due to truncation and round-off. Poisson's summation formulas are used to compute the Bessel equation of the first kind with arbitary small error.