ComposeSeries
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ComposeSeries
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 allclose allBasic Examples (2)Summary of the most common use cases
Properties & Relations (2)Properties of the function, and connections to other functions
ComposeSeries generates the series of composition of functions:
In[1]:=1

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https://wolfram.com/xid/0b8cm051a6-omb9rm
In[3]:=3

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https://wolfram.com/xid/0b8cm051a6-g3c3t8
In[5]:=5

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https://wolfram.com/xid/0b8cm051a6-sa920
Out[5]=5

In[6]:=6

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https://wolfram.com/xid/0b8cm051a6-dy7zza
Out[6]=6

Coefficients of the composition of series can be computed using BellY:
In[1]:=1

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https://wolfram.com/xid/0b8cm051a6-6z74g
Out[1]=1

In[2]:=2

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https://wolfram.com/xid/0b8cm051a6-e5yq7e
Out[2]=2

Wolfram Research (1996), ComposeSeries, Wolfram Language function, https://reference.wolfram.com/language/ref/ComposeSeries.html.
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Wolfram Research (1996), ComposeSeries, Wolfram Language function, https://reference.wolfram.com/language/ref/ComposeSeries.html.
Text
Wolfram Research (1996), ComposeSeries, Wolfram Language function, https://reference.wolfram.com/language/ref/ComposeSeries.html.
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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.
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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
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Wolfram Language. (1996). ComposeSeries. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ComposeSeries.html
BibTeX
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@misc{reference.wolfram_2025_composeseries, author="Wolfram Research", title="{ComposeSeries}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/ComposeSeries.html}", note=[Accessed: 03-June-2025
]}
BibLaTeX
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@online{reference.wolfram_2025_composeseries, organization={Wolfram Research}, title={ComposeSeries}, year={1996}, url={https://reference.wolfram.com/language/ref/ComposeSeries.html}, note=[Accessed: 03-June-2025
]}