This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# SeriesCoefficient

 SeriesCoefficientfinds the coefficient of the -order term in a power series in the form generated by Series. SeriesCoefficientfinds the coefficient of in the expansion of f about the point . SeriesCoefficientfinds a coefficient in a multivariate series.
• The following options can be given:
 Assumptions \$Assumptions assumptions to make about parameters Method Automatic method to use
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:
 Out[1]=
 Out[2]=

Find the coefficient of the general term in a series:
 Out[1]=
 Out[2]=
 Out[3]=

Find the coefficient for a term in a multivariate series:
 Out[1]=
 Out[2]=

Find the coefficient for a general term in a multivariate series:
 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 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:
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:
Series coefficients can be functions of the expansion variable:
General coefficients of series may not be available:
Series coefficient for a hypergeometric function: