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 , , whose , , 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:

In[1]:=
Click for copyable input
Out[1]=

All coefficients in the series are 1:

In[2]:=
Click for copyable input
Out[2]=

Univariate generating function:

In[1]:=
Click for copyable input
Out[1]=

Multivariate:

In[2]:=
Click for copyable input
Out[2]=

The generating function for a shifted sequence:

In[1]:=
Click for copyable input
Out[1]=
Introduced in 2008
(7.0)