On the Computation and Applications of Bessel Functions with Pure Imaginary Indices

TL;DR

This paper introduces a fast, efficient algorithm for computing Bessel functions with pure imaginary indices, which are crucial in optics and semiconductor material analysis.

Contribution

It presents a novel, rapid algorithm for calculating Bessel functions with pure imaginary order, improving computational speed and convergence for small arguments.

Findings

Algorithm is very fast to compute.

Converges after few iterations for small arguments.

Applicable in optics and semiconductor analysis.

Abstract

Bessel functions with pure imaginary index (order) play an important role in corpuscular optics where they govern the dynamics of charged particles in isotrajectory quadrupoles. Recently they were found to be of great importance in semiconductor material characterization as they are manifested in the strain state of crystalline material. A new algorithm which can be used for the computation of the normal and modifed Bessel functions with pure imaginary index is proposed. The developed algorithm is very fast to compute and for small arguments converges after a few iterations.