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.
Squaring the power series gives you another power series, with the appropriate number of terms.
truncates the power series, giving a normal expression.
You can now apply standard algebraic operations.
|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.
This gives the coefficient for the term xn
in the Taylor expansion of the function ex2