## 3.6.5 Converting Power Series to Normal Expressions

 Normal[expr] convert a power series to a normal expression

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]=

 SeriesCoefficient[series, n] give the coefficient of the order term in a power series

Extracting coefficients of terms in power series.
This gives the coefficient of in the original power series.
 In[5]:=  SeriesCoefficient[t, 7]
 Out[5]=

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