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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]=