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.

Details

Examples

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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:

Generalizations & Extensions  (1)

Invert a series, giving a result in terms of the variable y:

Applications  (2)

Find higher-order terms in Newton's approximation for a root of f[x] near :

Compute series expansion of at the origin, given :

Properties & Relations  (1)

Composing an inverse series with the original series gives the identity function:

Introduced in 1988
 (1.0)