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

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Basic Examples  (2)

Compose two power series:

Properties & Relations  (2)

ComposeSeries generates the series of composition of functions:

Coefficients of the composition of series can be computed using BellY:

Possible Issues  (1)

The limiting value of the second series must coincide with the expansion point of the first series:

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.

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_2024_composeseries, author="Wolfram Research", title="{ComposeSeries}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/ComposeSeries.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_composeseries, organization={Wolfram Research}, title={ComposeSeries}, year={1996}, url={https://reference.wolfram.com/language/ref/ComposeSeries.html}, note=[Accessed: 21-December-2024 ]}