Formally, we may use a change of variables again:

Then the model "factorizes" under the "change of variables"

To see this we consider the change of variables and , which makes sense if char.

Under this change of variables we rewrite to which, in turn, can be rewritten to .

This change of variables has two main advantages :

If characteristic were not an obstruction, each equation would reduce to the previous ones by a suitable change of variables.

In particular, it is not invariant under a change of variables and can even become negative.

By change of variables it is enough to prove the result there.

More concretely, their generating functions are equal after an appropriate change of variables.

To analyse this particular case further, consider the change of variables.