@Carl Love Thank you so much, the use of this procedure did indeed solve the issue.

However, I have two more questions please:

1) Putting local in both ux and ur gives me the following error "Error, invalid sequence". However, when I omit the definition of i as local, I get the following warnings "Warning, `i` is implicitly declared local to procedure `ux`,Warning, `i` is implicitly declared local to procedure `ur`". Is this related to the version of MAPLE I am using or something else ?

2) Is defining i in the constant A of the function ur using the procedure sufficent or is it needed to do the same thing for B ? In other words is there a difference between these two definitions:

ur:= r-> A[(local i:= op(procname))]*r + B[i]/r  

ur:= r-> A[(local i:= op(procname))]*r + B[(local i:= op(procname))]/r

Thank you again for your help !