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InverseSeries—Wolfram Documentation

Generalizations & Extensions  

InverseSeries[s]

takes the series s, and gives a series for the inverse of the function represented by s.

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:

History

Introduced in 1988 (1.0)

Wolfram Research (1988), InverseSeries, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseSeries.html.

Text

Wolfram Research (1988), InverseSeries, Wolfram Language function, https://reference.wolfram.com/language/ref/InverseSeries.html.

CMS

Wolfram Language. 1988. "InverseSeries." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InverseSeries.html.

APA

Wolfram Language. (1988). InverseSeries. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InverseSeries.html

BibTeX

@misc{reference.wolfram_2025_inverseseries, author="Wolfram Research", title="{InverseSeries}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/InverseSeries.html}", note=[Accessed: 22-February-2026]}

BibLaTeX

@online{reference.wolfram_2025_inverseseries, organization={Wolfram Research}, title={InverseSeries}, year={1988}, url={https://reference.wolfram.com/language/ref/InverseSeries.html}, note=[Accessed: 22-February-2026]}