Built-in Mathematica Symbol

SeriesData

SeriesData[x, x₀, {a₀, a₁, ...}, n_min, n_max, den]
represents a power series in the variable x about the point x₀. The a_i are the coefficients in the power series. The powers of (x-x₀) that appear are n_min/den, (n_min+1)/den, ... , n_max/den.

MORE INFORMATION

SeriesData objects are generated by Series.

SeriesData objects are printed as sums of the coefficients a_i, 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.