create the geometric series over a set of variables
variable, or nonempty list of variables
GeometricSeries(x) creates the geometric power series in x.
If x has more than one element then the result is the geometric series in the sum of the variables in x.
When using the MultivariatePowerSeries package, do not assign anything to the variables occurring in the power series, Puiseux series, and univariate polynomials over these series. If you do, you may see invalid results.
We create the geometric power series in x, that is, the power series for 11+x.
a ≔ GeometricSeries⁡x
a≔PowⅇrSⅇrⅈⅇs of 11−x : 1+x+…
If we truncate a at homogeneous degree 5, this is what we obtain.
We create the geometric power series in x+y, that is, the power series for 11+x+y.
b ≔ GeometricSeries⁡x,y
b≔PowⅇrSⅇrⅈⅇs of 11−x−y : 1+x+y+…
The homogeneous part of b of degree 4 is the following expression.
If we truncate b at homogeneous degree 3, this is what we obtain.
The MultivariatePowerSeries[GeometricSeries] command was introduced in Maple 2021.
For more information on Maple 2021 changes, see Updates in Maple 2021.
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