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holomorphic binary operators over naturals; generalized hyper operators
Right now I'm writing out some assumptions we have to put away.

For example:

This implies that is not analytic because it is 2 for all s with real part greater than or equal to 1 and 3 when s is 0.

Another one is that any continuous segment of operators is commutative or associative all the operators have to be. As well; operators in a continuous segment cannot have the same identity.

The functional requirement is the following:

where we have:

And is as before.

I can obtain as a taylor series using lagrange inversion. So all of these functions are theoretically computable besides which is in . So the requirement is restricted to it. I'm writing this all out trying to solve for the taylor series coefficients of . is entire if is entire; so I hope it is.

Thanks for the encouragement Gottfried. Like all math; it's slow progress. Little breakthroughs from time to time.

Messages In This Thread
RE: holomorphic binary operators over naturals; generalized hyper operators - by JmsNxn - 08/10/2012, 10:57 PM

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