BUILT-IN MATHEMATICA SYMBOL

ExponentialGeneratingFunction

gives the exponential generating function in x for the sequence whose n

term is given by the expression expr.

gives the multidimensional exponential generating function in

,

, ... whose

,

, ... term is given by expr.

MORE INFORMATION

The exponential generating function for a sequence whose term is is given by .

The multidimensional exponential 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

EXAMPLES

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Basic Examples (1)

The exponential generating function for the sequence whose n

term is 1:

The

term in the series is

:

The exponential generating function for the sequence whose n

term is 1:

In[1]:=

Out[1]=

The

term in the series is

:

In[2]:=

Out[2]=

Scope (7)

Univariate exponential generating function:

Multivariate:

Periodic sequences:

Polynomial:

Rational function:

Polynomial exponential:

Polynomial trigonometric:

Hypergeometric terms:

Special functions:

DifferenceRoot in general results in DifferentialRoot functions:

Generalizations & Extensions (1)

Compute the exponential generating function at a point:

Options (6)

In general this generating function cannot be given:

By providing additional Assumptions, an equivalent form can be given:

By default no conditions are given for where a generating function is convergent:

Use GenerateConditions to generate conditions of validity:

Different methods may produce different formulas:

Setting VerifyConvergence to False will treat generating functions as formal objects:

Setting VerifyConvergence to True will verify that the radius of convergence is nonzero:

In addition, setting GenerateConditions to True will display the conditions for convergence:

Properties & Relations (2)

ExponentialGeneratingFunction effectively computes an infinite sum:

Linearity:

Derivative: