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 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 .

Examples

open allclose all

Basic Examples(3)

The generating function for the sequence whose n term is 1:

 In[1]:=
 Out[1]=

All coefficients in the series are 1:

 In[2]:=
 Out[2]=

Univariate generating function:

 In[1]:=
 Out[1]=

Multivariate:

 In[2]:=
 Out[2]=

The generating function for a shifted sequence:

 In[1]:=
 Out[1]=