Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

GeneratingFunction

GeneratingFunction[expr,n,x]
gives the generating function in x for the sequence whose n 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

• The generating function for a sequence whose n term is an is given by .
• The multidimensional generating function is given by .
• The following options can be given:
•  Assumptions \$Assumptions assumptions to make about parameters GenerateConditions False whether to generate answers that involve conditions on parameters Method Automatic method to use VerifyConvergence True whether to verify convergence
• In TraditionalForm, GeneratingFunction is output using .

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

The generating function for the sequence whose n 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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