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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]= 
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