How does a generating function relate to a sequence of numbers.?

Answers

Answer #1 | 23/12 2013 20:44

Generating functions give a sequence of numbers by way of a power series. The coefficients of the series is the sequence of numbers. So for instance the generating function for the unit sequence {1,1,1,1,...} is
∑{n=0,∞} xⁿ = 1 / (1 - x)
The fact that the series has a closed form is convenient, but it's not required, and it's pretty rare.

Answer #1| 23/12 2013 20:44