# Probability generating function

#### Poirot

##### Banned
My question is : can a pgf have a constant term?

The reason I ask is that I was asked to show the (time) derivative of a pgf was equal to some multiple of the pgf and hence show the pgf was as given. So naturally , I differentiated the given answer and showed it satisfied the equation. But surely I could stick a constant on the end and it would differentiate to the same thing.

#### CaptainBlack

##### Well-known member
My question is : can a pgf have a constant term?

The reason I ask is that I was asked to show the (time) derivative of a pgf was equal to some multiple of the pgf and hence show the pgf was as given. So naturally , I differentiated the given answer and showed it satisfied the equation. But surely I could stick a constant on the end and it would differentiate to the same thing.