For solution see wordfile

This is brilliant, hans! I didn't know that poles and their orders can be found this way.

One question. In this solution, poles and their orders were first guessed, then proved. Does anybody know of a general procedure to arrive at these numbers without the guess work in the first place? Or is there any need for a general procedure at all?

To calculate the poles one has to calculate the zero’s of the denominator:

z^2.sin(az)=0
z=0 (2x) or sin(az)=0
z=0 2x) or az=kpi with k= ……,-3,-2,-1,0,1,2,3,….
z=0 (2x) or z= kpi/a
z=0 (3x) or z= kpi/a with k=….,-3,-2,-1,1,2,3,….