New Method for the Computation of Generating Functions with Applications

Generating functions (GFs) are one of the most useful tools for problem solving, as they have been playing an important role in many applications, including but not limited to counting, identity proving, analysis of algorithms, problem representation and solving in combinatorics. The authors have been studying a new transform called Sumudu Transform in a computational approach, in this work, it shall show that Sumudu Transform transfers the exponential generating functions to the ordinary generating functions and the transform also serves as a new powerful tool in the calculation of generating functions and applications. Applications include new methods in solving differential and integral equations automatically by using generating functions.