**Bivariate and Multivariate Generating Functions**

One can define generating functions in several variables for arrays with several indices. These are called **multivariate generating functions** or, sometimes, **super generating functions**. For two variables, these are often called **bivariate generating functions**.

For instance, since is the ordinary 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. Since the generating function for is, the generating function for the binomial coefficients is:

Read more about this topic: Generating Function, Ordinary Generating Functions

### Famous quotes containing the word functions:

“Empirical science is apt to cloud the sight, and, by the very knowledge of *functions* and processes, to bereave the student of the manly contemplation of the whole.”

—Ralph Waldo Emerson (1803–1882)