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Converting Power Series to Normal Expressions

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

Converting power series to normal expressions.

As discussed, 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.
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Squaring the power series gives you another power series, with the appropriate number of terms.
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Normal truncates the power series, giving a normal expression.
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You can now apply standard algebraic operations.
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SeriesCoefficient[series,n]give the coefficient of the nth order term in a power series

Extracting coefficients of terms in power series.

This gives the coefficient of x7 in the original power series.
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This gives the coefficient for the term xn in the Taylor expansion of the function ex2 about zero.
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