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Advanced Topic: Composition and Inversion of Power SeriesSolving Equations Involving Power Series

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]=

Advanced Topic: Composition and Inversion of Power SeriesSolving Equations Involving Power Series