I have a Stochastic Processes test coming up soon and we are taught about the first passage decomposition. I understand this but it then says that it changes it to a generating function
Generating function Pij(s) = Ʃ pij(n)sn
and Fij(s) = Ʃ fij(n)sn
What does this generating function actually mean and what is the difference between
Pij(s) and Fij(s)?