Examples of Generating Functions - Worked Example A: Basics

Worked Example A: Basics

New generating functions can be created by extending simpler generating functions. For example, starting with

and replacing with, we obtain

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Examples Of Generating Functions - Worked Example A: Basics - Bivariate Generating Functions
... For instance, since is the generating function for binomial coefficients for a fixed n, one may ask for a bivariate generating function that generates the binomial coefficients for all k and n ... To do this, consider as itself a series (in n), and find the generating function in y that has these as coefficients ...