Dear Mr. Dulgerci
It is a big surprise and pleasure to have gotten your reply!
I appreciate your answer a lot.
After using the function InterpolatingPolynomial I am not sure, though, as to whether or not my goals can be reached in mathematica or at all.
Please have a look at the document and tell me whether it is possible to achieve those goals. The interpolation is not giving me a very good fit on the targeted shape (paro2.nb).