When you manipulate power series, it is sometimes convenient to think of the series as representing functions
, which you can, for example, compose or invert.
If you have a power series for a function f (y)
, then it is often possible to get a power series approximation to the solution for y
in the equation f (y)=x
. This power series effectively gives the inverse function f-1 (x)
such that f (f-1 (x))=x
. The operation of finding the power series for an inverse function is sometimes known as reversion
of power series.