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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.
  • The generating function for a sequence whose n^(th) term is an is given by sum_(n=0)^(infty)a_n x^n.
  • The multidimensional generating function is given by .
  • The following options can be given:
Assumptions$Assumptionsassumptions to make about parameters
GenerateConditionsFalsewhether to generate answers that involve conditions on parameters
MethodAutomaticmethod to use
VerifyConvergenceTruewhether to verify convergence
EXAMPLESCLOSE ALL
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:
In[1]:=
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