Thanks a lot man, I really appreciate you're rooting for me. About the analysis, I'm sorry I've been not able to respond in the same level as before, but I get trapped with work almost everyday, but I'll sure check that when I have the proper time to do so.
haha no problem. that is a pretty cool function, and i agree euler's constant is interesting and useful. i wonder if there is an animation for a taylor series, that would look pretty cool as the series becomes more precise.