09/07/2007, 02:45 PM

andydude Wrote:I would love to talk to Walker about the super-logarithm, because as far as I know he was the first to consider an Abel function approximation as I have.You can do it, his e-mail is on his university page

http://www.aus.edu/cas/maths/staff/peter_walker.php

However my impression is that now as he is retired he is no more that engaged about the topic as he perhaps was earlier.

Quote:Also, the coefficients he gives for the natural (b=e) super-logarithm are identical (as far as approximations go) to my coefficients even though we use vastly different methods.

Peter Walker uses an iterated function in such a way that the infinite-fold iteration of that function represents an exact solution to the Abel function, and at the end of Walker's paper Infinitely Differentiable Generalized Logarithmic and Exponential Functions, he mentions that he has also tried a "matrix method" to obtain similar results, which I suspect is exactly the method that I found independently.

He writes in this paper that the coefficients for his first method differ from the coefficients he derived from the matrix method (which he quickly describes in this paper too).