07/19/2012, 10:16 PM

(07/19/2012, 04:44 PM)JmsNxn Wrote: We start by defining a sequence of analytic functions that obey the following rules:

and

Necessarily; these functions can be arbitrary and they pose the true uniqueness criterion. Nonetheless we suggest these functions and give a plausible solution.

Reason for this is it has fast convergence and satisfies the required conditions.

Now we perform a trick. Considering hyper operators; which are written by the following:

and the identity of for any natural is .

We get the usual sequence where zero is addition, one is multiplication, two is exponentiation, etc... We then write that complex operators are products of natural operators with complex exponents. Here; is as before.

Dont you need to prove the identity of the infinite product ?

e.g. does the infinite product formula hold for x + y and x*y ??

regards

tommy1729