represents a power series in the variable x about the point x0. The ai are the coefficients in the power series. The powers of (x-x0) that appear are nmin/den, (nmin+1)/den, …, nmax/den.
- SeriesData objects are generated by Series.
- SeriesData objects are printed as sums of the coefficients ai, multiplied by powers of x-x0. A SeriesData object representing a power series is printed with O[x-x0]^p added, to represent omitted higher‐order terms.
- When you apply certain mathematical operations to SeriesData objects, new SeriesData objects truncated to the appropriate order are produced.
- The operations you can perform on SeriesData objects include arithmetic ones, mathematical functions with built‐in derivatives, and integration and differentiation.
- Normal[expr] converts a SeriesData object into a normal expression, truncating omitted higher‐order terms.
- If the variable in a SeriesData object is itself a SeriesData object, then the composition of the SeriesData objects is computed. Substituting one series into another series with the same expansion parameter therefore automatically leads to composition of the series. Composition is only possible if the first term of the inner series involves a positive power of the variable.
- InverseSeries can be applied to SeriesData objects to give series for inverse functions.
Examplesopen allclose all
Basic Examples (1)
Construct SeriesData explicitly:
Rational powers are directly accounted for in SeriesData:
Symbolic powers are kept outside SeriesData:
Rapidly increasing or oscillating functions are kept outside SeriesData: