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 OptionsDetails and Options

ExamplesExamplesopen allclose all

Basic Examples  (3)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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Introduced in 2008
(7.0)