Working with Power Series

Axiom has very sophisticated facilities for working with power series. Infinite series are represented by a list of the coefficients that have already been determined, together with a function for computing the additional coefficients if needed. The system command that determines how many terms of a series is displayed is

      )set streams calculate

By default Axiom will display ten terms. Series can be created from expressions, from functions for the series coefficients, and from applications of operations on existing series. The most general function for creating a series is called series, although you can also use taylor, laurent, and puiseux in situations where you know what kind of exponents are involved. For information about solving differential equations in terms of power series see Power Series Solutions of Differential Equations

- Creation of Power Series
- Coefficients of Power Series
- Power Series Arithmetic
- Functions on Power Series
- Converting to Power Series
- Power Series from Formulas
- Substituting Numerical Values in Power Series
- Example: Bernoulli Polynomials and Sums of Powers