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ComposeSeries

  • ComposeSeries[ , , ... ] composes several power series.
  • ComposeSeries[ , , ... ] effectively replaces the variable in by and so on.
  • Two series can only meaningfully be composed when the point about which the first series is expanded corresponds to the limiting value of the second series at its expansion point.
  • See the Mathematica book: Section 3.6.4.
  • See also: InverseSeries.

    Further Examples

    This gives the series for the sine function about up to the order term.

    In[1]:=

    Out[1]=

    Here is a series involving cosine.

    In[2]:=

    Out[2]=

    This gives the composition of the two series.

    In[3]:=

    Out[3]=

    In[4]:=