Definition:Generating Function/Historical Note

Historical Note on Generating Function
Generating functions were introduced by to solve the general problem of linear recurrences.

then extended this theory in his of $1730$, by using differentiation and integration.

Then began extending their use to new fields such as combinatorics.

took the technique into the field of probability theory in his $1812$ work

Many others since have developed the technique further.


 * A generating function is a clothesline on which we hang up a sequence of numbers for display.