Exponentiate a power series or a univariate polynomial over power series
power series generated by this package
univariate polynomial over power series generated by this package
The commands p^e and Exponentiate(p,e) exponentiate the power series p by raising it to the power e.
The commands u^n and Exponentiate(u,n) exponentiate the univariate polynomial over power series u by raising it to the power n.
Note that power series can be raised to any integer power, whereas univariate polynomials over power series can only be raised to nonnegative integer powers.
When using the MultivariatePowerSeries package, do not assign anything to the variables occurring in the power series and univariate polynomials over power series. If you do, you may see invalid results.
We define a power series, a.
We can define a4 in three different ways: using multiplication, using the exponentiation operator, or using the Exponentiate command.
c≔PowⅇrSⅇrⅈⅇs of 11−x−y4 : 1+4⁢x+4⁢y+…
d≔PowⅇrSⅇrⅈⅇs of 11−x−y4 : 1+4⁢x+4⁢y+…
We verify that the homogeneous components of b, c, and d of degree at most 10 are the same.
We define a univariate polynomial over power series, f.
Again, we can define f3 in three different ways. We verify that they give the same result (at least for degrees at most 10).
The MultivariatePowerSeries[Exponentiate] command was introduced in Maple 2021.
For more information on Maple 2021 changes, see Updates in Maple 2021.
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