bo198214 Wrote:Excellent questions, however can you prove your "facts"?

Or are they the outcome of numerical experiments?

I do not have objective to give formal proof for these statements. But I’ve checked statements by using Taylor formula and induction process to calculate first four coefficients and residue in resulting series. This check is not very hard exercise, if you interested, please, verify. Then I have made numerical check. So there is chance to choose corresponding function.. may be it is possible to choose quite simple function, may be not...

My questions are what I am interesting, no more. I have made posting because I like this forum and article in Wikipedia, it is very interesting, thanx.