represents a term of order xn.
is generated to represent omitted higher‐order terms in power series.
represents a term of order (x-x0)n.
- Normal can be used to truncate power series, and remove O terms.
Examplesopen allclose all
Basic Examples (1)
A series representing an approximate function:
Doing operations on the approximate function maintains the appropriate series order:
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:
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: