This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# ExponentialGeneratingFunction

 ExponentialGeneratingFunction gives the exponential generating function in x for the sequence whose n term is given by the expression expr. ExponentialGeneratingFunctiongives the multidimensional exponential generating function in , , ... whose , , ... term is given by expr.
• 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
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:
 Out[1]=
The term in the series is :
 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:
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:
ExponentialGeneratingFunction effectively computes an infinite sum:
Linearity:
Derivative:
New in 7