08/13/2007, 10:30 PM

I've been looking at some graphs of the root-test: for the coefficients of fractional-iterates of the natural decremented exponential, and I'm starting to believe Baker over Walker, i.e., that it does in fact diverge for non-integers.

Here are the graphs, (using ):

In order for these functions to converge, the root-test must be bounded, and as you can see the non-integer root-tests seem to be unbounded, supporting Baker.

Andrew Robbins

Here are the graphs, (using ):

- DE^[-3/2](x)

- DE^[-1](x)

- DE^[-1/2](x)

- x (omitted)

- DE^[1/2](x)

- DE(x)

- DE^[3/2](x)

In order for these functions to converge, the root-test must be bounded, and as you can see the non-integer root-tests seem to be unbounded, supporting Baker.

Andrew Robbins