represents a term of order xn.


is generated to represent omitted higherorder terms in power series.


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


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


open allclose all

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:

Introduced in 1988