O

O[x]^n

represents a term of order xn.

O[x]^n

is generated to represent omitted higher‐order terms in power series.

O[x,x0]^n

represents a term of order (x-x0)n.

Details

  • Normal can be used to truncate power series, and remove O terms.

Examples

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Basic Examples  (1)

A series representing an approximate function:

Doing operations on the approximate function maintains the appropriate series order:

Scope  (2)

Like approximate numbers, approximate functions are contagious:

O can be used to drop higher-order terms:

Generalizations & Extensions  (3)

O[x,x0] represents a term with expansion point x0:

With expansion point ∞, the effective variable is :

An expression involving O is converted to a SeriesData object:

Applications  (1)

Find the lowest-order terms in a large polynomial:

Properties & Relations  (1)

Applying a function may give a different number of terms than generating the series from scratch:

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

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2024_o, author="Wolfram Research", title="{O}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/O.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_o, organization={Wolfram Research}, title={O}, year={1988}, url={https://reference.wolfram.com/language/ref/O.html}, note=[Accessed: 21-December-2024 ]}