Converting Power Series to Normal Expressions

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 higher-order terms are zero.

This generates a power series, with four terms:

t=Series[ArcTan[x],{x,0,8}]

Squaring the power series gives you another power series, with the appropriate number of terms:

t^2

(RefLink[Normal, paclet:ref/Normal]) truncates the power series, giving a normal expression:

Normal[%]

You can now apply standard algebraic operations:

Factor[%]

Extracting coefficients of terms in power series.

This gives the coefficient of (x^7) in the original power series:

SeriesCoefficient[t,7]

This gives the coefficient for the term (x^n) in the Taylor expansion of the function (e^(x^2)) about zero:

SeriesCoefficient[E^x^2,{x,0,n}]