ExponentialGeneratingFunction

ExponentialGeneratingFunction[expr,n,x]

gives the exponential generating function in x for the sequence whose n^(th) term is given by the expression expr.

ExponentialGeneratingFunction[expr,{n1,n2,},{x1,x2,}]

gives the multidimensional exponential generating function in x1, x2, whose n1, n2, term is given by expr.

Details and Options

  • The exponential generating function for a sequence whose ^(th) term is is given by .
  • The multidimensional exponential 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

Examples

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Basic Examples  (1)

The exponential generating function for the sequence whose n^(th) term is 1:

In[1]:=
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Out[1]=

The ^(th) term in the series is :

In[2]:=
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Out[2]=

Scope  (7)

Generalizations & Extensions  (1)

Options  (5)

Properties & Relations  (3)

Possible Issues  (1)

Neat Examples  (1)

See Also

GeneratingFunction  D  Series  SeriesCoefficient  Sum  ZTransform  RSolve

Introduced in 2008
(7.0)