Converting Power Series to Normal Expressions

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

Converting power series to normal expressions.

Power series in the Wolfram Language 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 higherorder terms are zero.

This generates a power series, with four terms.
In[1]:=
Click for copyable input
Out[1]=
Squaring the power series gives you another power series, with the appropriate number of terms.
In[2]:=
Click for copyable input
Out[2]=
Normal truncates the power series, giving a normal expression.
In[3]:=
Click for copyable input
Out[3]=
You can now apply standard algebraic operations.
In[4]:=
Click for copyable input
Out[4]=
SeriesCoefficient[series,n]give the coefficient of the n^(th) 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]:=
Click for copyable input
Out[5]=
This gives the coefficient for the term in the Taylor expansion of the function about zero.
In[6]:=
Click for copyable input
Out[6]=