Towards a general theory of special functions
Communications of the ACM
Symbolic integration of a class of algebraic functions
ACM SIGSAM Bulletin
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An example of a multiple-scale perturbation expansion using the MACSYMA algebraic manipulation system is derived. The problem solved is a differential equation for a linear damped oscillator, whose closed form solution can be easily compared to the generated approximation. The advantages of the automatic approach include, especially in more difficult cases, the rapid computation of higher order terms by computer, complete accuracy in algebra, and automatic and accurate conversion of the formulas to graphical or numerical form. Among the unusual features used is MACSYMA's ability to solve in closed form, elementary ordinary differential equations.