finds the coefficient of the n ^(th)-order term in a power series in the form generated by Series.


finds the coefficient of in the expansion of f about the point .


finds a coefficient in a multivariate series.

Details and Options


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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:

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)

Assumptions  (2)

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:

Method  (1)

This generates a DifferenceRoot object when possible:

Applications  (4)

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 y[n]:

Use RSolve:

Find the coefficient of the general term in the power series expansion of 1/(1+x):

Obtain the power series expansion in Inactive form:

Make a table of the power series expansions for different functions:

Properties & Relations  (4)

Use DiscreteAsymptotic to compute an asymptotic approximation:

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  (2)

Series coefficient for a hypergeometric function:

Create a gallery of common series coefficients:

Introduced in 1996
Updated in 2007