06/06/2011, 09:23 AM

(06/06/2011, 08:47 AM)JmsNxn Wrote: I was sort of aware that there was no way I was gonna produce an analytic function over the whole complex domain, I'm happy with analytic in a few regions.Well not on the whole complex plane, but on the real axis, wouldnt that be nice?

I anyway wonder whether thats possible at all.

As is not even differentiable at 1, I wonder whether f is. Did you compare the derivations from left and right?

Quote:Alright, from henceforth I shall refer to logarithmic semi operators with the following notation:

oh I thought }t{ was kinda the inverse in t. But as I see that it is not ... there are already conventions that we use on the forum, even ASCII capable:

a [1] b = a+ b

a [2] b = a*b

a [3] b = a^b

so the operator is [t] (one off from your {t}). But then for the inverse functions

b [t] x = y

y /[t] x = b

b [t]\ y = x

for example

x /[1] y = x - y

x [1]\ y = -x + y

x /[4] p is the p-th superroot (which is not equal to x [4] 1/p)

b [4]\ x is the superlogarithm to base b.

This is also in sync with the convention for quasigroups, i.e. groups with non-associative operation but with left- and right-inverse. There the left- and right inverse are written as / and \.