Many problems in mathematical physics, especially in quantum mechanics, are solved in terms of functions that are no longer elementary. Trigonometric functions, such as sine and cosine, are examples of elementary functions. On the other hand, Bessel functions, which appear as solutions of many problems of wave propagation, are examples of special functions that require their own study and investigation. In my summer research, I worked with a more complicated class of functions known as Appell hypergeometric functions that appear as solutions of many problems in radiation physics. This class of functions is expressed as a double infinite series that is not possible to calculate in general. My research focused on simplifying this function in more elementary terms that make it simpler to use and analyze. My investigation allowed me to tabulate the simplified expressions of this function for certain values of its parameters. Specific results useful for analyzing many problems in radiation field theory are now in progress.

I was drawn to this research by its sense of importance. I could feel the utility of each result, and it excites me to consider other people making use of my simplifications. As a bonus, I enjoyed the challenge of playing around with the expressions to find the best simplifications.