02/20/2013, 11:30 AM
mike3 Wrote:Then you'll probably like the Kneser method more than Robbins' one. Robbins' only works for a limited range of complex heights since it creates a Taylor series in the height, which is limited by the singularities (and also, quasi-limited by the area of very rapid growth).
But the problem with kneser is that it requires some time to calculate the polynomials and set-up with the base. I need a code that can continuously output sexp(b, z) for different bases. For example, if I use code Sheldon created and want to calculate sexp(2, 0.5) + sexp(3, 0.5) then it isn't possible to directly command PARI to do that. We need to write init(2);sexp(0.5) and init(3);sexp(0.5) differently and then sum the results up. But consider that we need to do this several times. Then it is impossible by this algorithm. But I think Robbins' method doesn't requires the use of initializing the base(?). It's okay if limited, real values would do the thing.
mike3 Wrote:What commands are you using to give tetration? What commands did you use to get that value? As when I use it, PARI/GP returns a "*** log: zero argument in mplog" error -- which is what I'd expect, since there's a singularity. I use "init(2)" then "loop(<some number of loops>)" then "sexp(-3)". Perhaps you missed a command or used the wrong one?
I am using the code "kneser.gp" that I downloaded from here somewhere. It doesn't gives me any error, just returns the complex value I posted before. I typed init(2) then loop(6) and at last sexp(-3). It returns the same, ~6.73 + i*4.53
mike3 Wrote:I'm curious: what exactly are you trying to do with this, anyway?
I mentioned before that I am working on a function. But I am currently too shy to give it away since I haven't succeeded to get any possible properties of the function
