ComposeSeries[series1,series2,…]
composes several power series.


ComposeSeries
ComposeSeries[series1,series2,…]
composes several power series.
Details

- ComposeSeries[series1,series2,…] effectively replaces the variable in series1 by series2 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.
Examples
open all close allProperties & Relations (2)
ComposeSeries generates the series of composition of functions:
Coefficients of the composition of series can be computed using BellY:
See Also
Related Guides
History
Introduced in 1996 (3.0)
Text
Wolfram Research (1996), ComposeSeries, Wolfram Language function, https://reference.wolfram.com/language/ref/ComposeSeries.html.
CMS
Wolfram Language. 1996. "ComposeSeries." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ComposeSeries.html.
APA
Wolfram Language. (1996). ComposeSeries. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ComposeSeries.html
BibTeX
@misc{reference.wolfram_2025_composeseries, author="Wolfram Research", title="{ComposeSeries}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/ComposeSeries.html}", note=[Accessed: 08-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_composeseries, organization={Wolfram Research}, title={ComposeSeries}, year={1996}, url={https://reference.wolfram.com/language/ref/ComposeSeries.html}, note=[Accessed: 08-August-2025]}