Electrons driven by intense laser fields exhibit nonlinear Thomson scattering. Measuring these radiation patterns has become of interest to many groups including our group at Brigham Young University.The theoretical description of this phenomenon was outlined by Sarachik and Schappert in 1970. The solution for the scattered light involves a numeric integral. They developed an approximation which uses a series of Bessel functions in place of the integral. In this thesis we investigate the efficacy of the Bessel-series approximation to see if gives an advantage over the numerical-integration approach. We find only a modest advantage for certain parameters. Generally, performing the integration numerically is a sensible approach.