BUILT-IN MATHEMATICA 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 , , ... whose , , ... coefficient is given by expr.

## Details and OptionsDetails and Options

• The generating function for a sequence whose n term is 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:

 Out[1]=

All coefficients in the series are 1:

 Out[2]=

Univariate generating function:

 Out[1]=

Multivariate:

 Out[2]=

The generating function for a shifted sequence:

 Out[1]=