I have been unable to post stuff thanks to my new friends called multivalued funtions and brach which have been keeping from doing any progress on my research. So next time you use any of these multivalued function (i.e. the arcsin(x)) stop to think about it for a second, I will.
I'm working on the second part of the linked list post, that should come out soon. Also this month on the cise publication the article "On the evaluation of Finite Hilbert Transforms" proposes the double exponential method as a good numeric method to find Hilbert Transforms. I talked about Hilbert Transforms before, and I use them in my research so I will implement the method and publish the code on here.
One more thing. This is just a mathematical curiosity. I was trying to calculate the derivate of x^x, as it turns out you can take the natural log on both sides of the equation before taking the derivative. I get ln(x^x) = ln(x*x*x*...) = x*ln(x) but this bugs me since x doesn't have to be an integer. Any ideas?