Mathematica Tutorial

Converting Power Series to Normal Expressions

convert a power series to a normal expression

Converting power series to normal expressions.

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 n^th 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 e^x² about zero.

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