Definition:Generating Function/Parameter

Definition

Let $\map {G_A} z$ be a generating function for the sequence $A$.

The variable $z$ is a dummy variable, known as the parameter of $\map {G_A} z$.

Also denoted as

The symbol used for the parameter varies.

$x$ is often used instead.

In the field of probability theory $s$ tends to be the symbol of choice.

Some authors use $\zeta$.

Sources

• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.9$: Generating Functions