axiom-hypertex-data 20120501-8 / usr / share / doc / axiom-doc / hypertex / calseries.xhtml

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 <head>
  <meta http-equiv="Content-Type" content="text/html" charset="us-ascii"/>
  <title>Axiom Documentation</title>
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 <body>
  <div align="center"><img align="middle" src="doctitle.png"/></div>
  <hr/>
  <div align="center">Working with Power Series</div>
  <hr/>
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
<pre>
  )set streams calculate
</pre>
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 <a href="dbopseries.xhtml">series</a>, although you can
also use 
<a href="dboptaylor.xhtml">taylor</a>,
<a href="dboplaurent.xhtml">laurent</a>, and
<a href="dboppuiseux.xhtml">puiseux</a> in situations where you know what 
kind of exponents are involved.

For information about solving differential equations in terms of power
series see
<a href="axbook/section-8.10.xhtml#subsec-8.10.3">
Power Series Solutions of Differential Equations</a>
<ul>
 <li>
  <a href="calseries1.xhtml">
   Creation of Power Series
  </a>
 </li>
 <li>
  <a href="calseries2.xhtml">
   Coefficients of Power Series
  </a>
 </li>
 <li>
  <a href="calseries3.xhtml">
   Power Series Arithmetic
  </a>
 </li>
 <li>
  <a href="calseries4.xhtml">
   Functions on Power Series
  </a>
 </li>
 <li>
  <a href="calseries5.xhtml">
   Converting to Power Series
  </a>
 </li>
 <li>
  <a href="calseries6.xhtml">
   Power Series from Formulas
  </a>
 </li>
 <li>
  <a href="calseries7.xhtml">
   Substituting Numerical Values in Power Series
  </a>
 </li>
 <li>
  <a href="calseries8.xhtml">
   Example: Bernoulli Polynomials and Sums of Powers
  </a>
 </li>
</ul>
 </body>
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