In my university the z transfrom's time delay property also called shifting property is shown as follows $$Z[f(k - n)] = z^{-n}F(z) = z^{-n} \sum\limits_{k=-\infty}^{\infty}f(k)z^{-k}$$
but according to this website https://coertvonk.com/physics/lfz-transforms/z/properties-proofs-22533
The guy proves the time delay property for 2 cases
- When $ (n-a) < 0$ is not defined (it is my understanding after comparing the cases)
- When $ (n-a) < 0$ exists or is defined
But the limits used by this guy are k = 0 to k = $\infty$ unlike the one I have learnt in my course.
I don't understand which is the correct one or if both are correct then what is the difference between the 2