Definition:Generating Function/Also denoted as

Generating Function: Also denoted as

When the sequence is understood, the notation $\map G z$ can be used for its generating function.

Different authors may use different symbols for $G_A$, for example:

$\map {f_A} z$

$\map U s$

$\map A x$

$\map {\mathrm f} t$

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 $\zeta$, and some use $t$.

Sources

• 1956: G. Pólya: On Picture-Writing (Amer. Math. Monthly Vol. 63: pp. 689 – 697)  www.jstor.org/stable/2309555
• 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {3-4}$ Generating Functions: Definition $\text {3-3}$
• 1986: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction ... (previous) ... (next): $\S 4.1$: Generating functions
• 1994: Herbert S. Wilf: generatingfunctionology (2nd ed.)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): generating function
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): generating function