gives the generating function in x for the sequence whose n series coefficient is given by the expression expr.
gives the multidimensional generating function in x1, x2, … whose n1, n2, … coefficient is given by expr.
Details and Options
- The generating function for a sequence whose n term is an is given by .
- The multidimensional 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
- In TraditionalForm, GeneratingFunction is output using .
Examplesopen allclose all
Basic Examples (3)
Basic Uses (7)
Plot the spectrum in the complex plane using ParametricPlot3D:
GeneratingFunction will use several properties including linearity:
GeneratingFunction automatically threads over lists:
Special Sequences (12)
The DiscreteRatio is rational for all hypergeometric term sequences:
By providing additional Assumptions, a closed form can be given:
Use GenerateConditions to generate conditions of validity:
Properties & Relations (5)
Use SeriesCoefficient to get the sequence from its generating function:
GeneratingFunction effectively computes an infinite sum:
Possible Issues (1)
Wolfram Research (2008), GeneratingFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/GeneratingFunction.html.
Wolfram Language. 2008. "GeneratingFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GeneratingFunction.html.
Wolfram Language. (2008). GeneratingFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GeneratingFunction.html