Answer to Question #153162 in Classical Mechanics for Afraid

Question

Explain generating function.

Answer 1

The function which provides the method to solve the recurrence relation that is called Generating function.

Let G(t) is a series $G(t)=a_ot^0+a_1t^1+a_2t^2+a_3t^3+......a_nt_n$

Here, $a_o a_1, a_2, a_3....$ etc are real number.

So, here G(t) is called generating function of sequence $a_r.$

For constant sequence 1,1, 1, 1 ... the generating function is

$G(t)=\frac{1}{1-t}$

So, we can express it as $G(t)=(1-t)^{-1}=1+t+t^2+t^3+.......$