This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

Documentation / Mathematica / The Mathematica Book / Advanced Mathematics in Mathematica / Series, Limits and Residues /

3.6.5 Converting Power Series to Normal Expressions

Converting power series to normal expressions.

As discussed above, power series in Mathematica are represented in a special internal form, which keeps track of such attributes as their expansion order.

For some purposes, you may want to convert power series to normal expressions. From a mathematical point of view, this corresponds to truncating the power series, and assuming that all higher-order terms are zero.

This generates a power series, with four terms.

In[1]:= t = Series[ ArcTan[x], {x, 0, 8} ]

Out[1]=

Squaring the power series gives you another power series, with the appropriate number of terms.

In[2]:= t^2

Out[2]=

Normal truncates the power series, giving a normal expression.

In[3]:= Normal[%]

Out[3]=

You can now apply standard algebraic operations.

In[4]:= Factor[%]

Out[4]=

Extracting coefficients of terms in power series.

This gives the coefficient of in the original power series.

In[5]:= SeriesCoefficient[t, 7]

Out[5]=