An investigation of a stable numerical algorithm for the evaluation of fractional order Bessel functions.

Abstract

For the evaluation of Bessel functions of integer orders, many good algorithms have been proposed. However, the computation of Bessel functions of fractional orders presents difficulties. In Numerical Recipes [10], there is an efficient routine for the numerical approximation of Bessel functions of fractional orders. This thesis will analyze this algorithm. The method uses continued fractions to evaluate Bessel functions of fractional orders. Chapter 1 is the introduction to Bessel functions. Chapter 2 describes a specific application of Bessel functions of fractional orders. Chapter 3 provides background material the student of continued fractions and Chapter 4 analyzes the algorithm.