GeneratingFunction

GeneratingFunction[expr,n,x]

gives the generating function in x for the sequence whose n^(th) series coefficient is given by the expression expr.

GeneratingFunction[expr,{n1,n2,},{x1,x2,}]

gives the multidimensional generating function in x1, x2, whose n1, n2, coefficient is given by expr.

Details and Options

Examples

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Basic Examples  (3)

The generating function for the sequence whose n^(th) term is 1:

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All coefficients in the series are 1:

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Univariate generating function:

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Multivariate:

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The generating function for a shifted sequence:

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Scope  (4)

Generalizations & Extensions  (1)

Options  (6)

Properties & Relations  (5)

Possible Issues  (1)

Neat Examples  (1)

See Also

Series  SeriesCoefficient  Sum  ZTransform  DiscreteConvolve  RSolve  ExponentialGeneratingFunction  FindGeneratingFunction

Introduced in 2008
(7.0)