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DOCUMENTATION CENTER SEARCH
Mathematica
>
Built-in
Mathematica
Symbol
Symbolic Mathematics: Basic Operations
Power Series
Making Power Series Expansions
Operations on Power Series
The Representation of Power Series
Converting Power Series to Normal Expressions
Tutorials »
|
SeriesCoefficient
InverseSeries
ComposeSeries
Limit
Normal
InverseZTransform
RSolve
O
SeriesData
PadeApproximant
FourierSeries
See Also »
|
Analytic Number Theory
Calculus
Manipulating Equations
Multiplicative Number Theory
Series Expansions
New in 6.0: Mathematics & Algorithms
More About »
Series
Series
[
f
, {
x
,
x
0
,
n
}]
generates a power series expansion for
f
about the point
x
=
x
0
to order
(
x
-
x
0
)
n
.
Series
[
f
, {
x
,
x
0
,
n
x
}, {
y
,
y
0
,
n
y
},
...
]
successively finds series expansions with respect to
x
, then
y
, etc.
MORE INFORMATION
Series
can construct standard Taylor series, as well as certain expansions involving negative powers, fractional powers and logarithms.
Series
detects certain essential singularities.
On
[Series::
esss
]
makes
Series
generate a message in this case.
Series
can expand about the point
x
=
.
Series
[
f
, {
x
, 0,
n
}]
constructs Taylor series for any function
f
according to the formula
.
Series
effectively evaluates partial derivatives using
D
. It assumes that different variables are independent.
The result of
Series
is usually a
SeriesData
object, which you can manipulate with other functions.
Normal
[
series
]
truncates a power series and converts it to a normal expression.
SeriesCoefficient
[
series
,
n
]
finds the coefficient of the
n
-order term.
EXAMPLES
CLOSE ALL
Basic Examples
(3)
Power series for the exponential function around
:
In[1]:=
Out[1]=
Convert to a normal expression:
In[2]:=
Out[2]=
Power series of an arbitrary function around
:
In[1]:=
Out[1]=
In[1]:=
Out[1]=
In any operation on series, only appropriate terms are kept:
In[2]:=
Out[2]=
Scope
(10)
Generalizations & Extensions
(4)
Options
(4)
Applications
(8)
Properties & Relations
(9)
Possible Issues
(6)
SEE ALSO
SeriesCoefficient
InverseSeries
ComposeSeries
Limit
Normal
InverseZTransform
RSolve
O
SeriesData
PadeApproximant
FourierSeries
TUTORIALS
Symbolic Mathematics: Basic Operations
Power Series
Making Power Series Expansions
Operations on Power Series
The Representation of Power Series
Converting Power Series to Normal Expressions
RELATED LINKS
Demonstrations with Series
(
Wolfram Demonstrations Project
)
Implementation notes: Algebra and Calculus
NKS|Online
(
A New Kind of Science
)
MORE ABOUT
Analytic Number Theory
Calculus
Manipulating Equations
Multiplicative Number Theory
Series Expansions
New in 6.0: Mathematics & Algorithms
New in 1 | Last modified in 3