That is right conditioned when k and z(x) are both positive. Actually it is a bit fussy to check a global converge. I am not sure exactly when it converges. That is why I want to surpass the convergence issue, if there is any way. Its kind of saying that, I do not want to bother about the convergence, yet calculate the limiting values and then develop something for convergence. (If it can be done or makes sense. I am still thinking about it. Not so sure about my perspectives and conclusions.)