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InverseSeries

InverseSeries[s]
takes the series s, and gives a series for the inverse of the function represented by s.
InverseSeries[s, x]
uses the variable x in the inverse series.
  • Given a series s(y), InverseSeries[s, x] gives a series for y such that s(y)=x.
EXAMPLESCLOSE ALL
Basic Examples   (3)
Find a series for the inverse function of x Sin[x]:
Find a series for the inverse function of Sin[x]:
Find the series for the inverse of the function represented by an explicitly specified series:
Invert again to get back the original function:
Find a series for the inverse function of x Sin[x]:
In[1]:=
Click for copyable input
Out[1]=
 
Find a series for the inverse function of Sin[x]:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Find the series for the inverse of the function represented by an explicitly specified series:
In[1]:=
Click for copyable input
Out[1]=
Invert again to get back the original function:
In[2]:=
Click for copyable input
Out[2]=
Generalizations & Extensions   (1)
Invert a series, giving a result in terms of the variable y:
Applications   (1)
Find higher-order terms in Newton's approximation for a root of f[x] near x=a:
Properties & Relations   (1)
Composing an inverse series with the original series gives the identity function:
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