Mathematica 9 is now available
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
New to Mathematica? Find your learning path »
Mathematica >
BUILT-IN MATHEMATICA SYMBOLTutorials »|See Also »|More About »

SeriesCoefficient

SeriesCoefficient
finds the coefficient of the ^(th)-order term in a power series in the form generated by Series.
SeriesCoefficient
finds the coefficient of in the expansion of f about the point .
SeriesCoefficient
finds a coefficient in a multivariate series.
MORE INFORMATION
  • The following options can be given:
Assumptions$Assumptionsassumptions to make about parameters
MethodAutomaticmethod to use
EXAMPLESCLOSE ALL
Basic Examples   (4)
Find the coefficient for a term in a series:
Find the coefficient of the general term in a series:
Find the coefficient for a term in a multivariate series:
Find the coefficient for a general term in a multivariate series:
Find the coefficient for a term in a series:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Find the coefficient of the general term in a series:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=
 
Find the coefficient for a term in a multivariate series:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Find the coefficient for a general term in a multivariate series:
In[1]:=
Click for copyable input
Out[1]=
Scope   (6)
Compute a series coefficient:
Plot the resulting sequence:
Rational functions:
Elementary functions:
Special functions:
In general a DifferenceRoot function may be required to express the solution:
Find the coefficients in multivariate functions:
Options   (3)
Coefficients of the expansion of the Chebyshev polynomials:
Use Assumptions to get a simpler result:
With no Assumptions, general results are generated:
With Assumptions a result valid under the given assumptions is given:
This generates a DifferenceRoot object when possible:
Applications   (3)
Find the 11^(th) Fibonacci number from its generating function:
Find a Chebyshev polynomial from its generating function:
Solve a linear difference equation:
Add the initial value equation and solve the algebraic equation for the transform:
Find the expression for :
Use RSolve:
Properties & Relations   (3)
The coefficients of a truncated series expansion:
The general coefficient formula:
The general formula agrees with the truncated expansion:
CoefficientList finds all coefficients in a series:
SeriesCoefficient is closely related to InverseZTransform:
Possible Issues   (2)
Series coefficients can be functions of the expansion variable:
General coefficients of series may not be available:
Neat Examples   (1)
Series coefficient for a hypergeometric function:
New in 3 | Last modified in 7
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team
Format:   HTML  |  CDF