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Series
Series[
f
,
x
,
,
n
] generates a power series expansion for f about the point  to order  .
Series[
f
,
x
,
,
,
y
,
,
] successively finds series expansions with respect to y, then x.
Series can construct standard Taylor series, as well as certain expansions involving negative powers, fractional powers and logarithms.
Series detects certain essential singularities.
Series can expand about the point  .
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 
 order term.
See the Mathematica book: Section 1.5.9, Section 3.6.1.
See also Implementation NotesA.9.55.17MainBookLinkOldButtonDataA.9.55.17.
See also: InverseSeries, ComposeSeries, Limit, Normal.
Related packages: Calculus`Pade`, NumericalMath`Approximations`, DiscreteMath`RSolve`.
Further Examples
This gives the general Taylor series up to the fifth degree term for a function f.
In[1]:= 
Out[1]= 
Here is a series for  .
In[2]:= 
Out[2]= 
You can do arithmetic on series objects.
In[3]:= 
Out[3]= 
This gives a series for a function of two variables.
In[4]:= 
Out[4]= 
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