Algorithms for series coefficients
The expansion of Taylor series is a very old topic in both pure and applied mathematics. It plays a crucial role in fundamental theory and applications. Computer algebra systems provide an interactive environment to assist in solving many mathematical problems. This work focuses on the development of techniques and algorithms for determining the coefficients in the Taylor expansion of a function. Our goal is to provide a set of procedures that can be implemented with these systems.
In this work, by comparing coefficients and taking derivatives, we develop some new methods called exact methods. We introduce transform methods, which is based on Laplace transformation, and discuss asymptotic methods, which is based on Integration.
The algorithms we developed are capable of obtaining closed forms and asymptotic information for a much wider class of functions than is possible using current techniques and existing theories. Furthermore, we will be able to demonstrate the superiority of our methods by implementing them using the Maple computer algebra system and comparing the results with those obtained by others.
0984: Computer science