| Abstract: | The creation, manipulation and evaluation of univariate infinite power series is discussed. Unlike truncated power series, which store the first n terms of an expansion, infinite power series create a procedure for calculating a general term, and are thus a formal representation of the entire expansion. No term is calculated until it is actually needed. All results may be saved along with the environment in which they were evaluated in order to prevent repeated calculation. Laurent expansion is used, and expansion in rational powers is allowed to expand expressions containing poles and branch points. The formulas applicable to the manipulation of these extended series forms are presented. The system is implemented in MODE-REDUCE with infinite power series a new data type, or mode, which allows interfacing with the usual algebraic operators including substitution, differentiation, and integration. A series may also be inverted. Examples of the capabilities and use of the system are presented. |
