tommy's "linear" summability method

[tommy1729]

The link Caleb gave ( https://mathoverflow.net/questions/43869...tical-cont ) me reminded me of this

https://math.stackexchange.com/questions...0-ns-n-s-1

which I posted here too.

The other link he gave :

https://mathoverflow.net/questions/19866...871#198871

There is alot to say about such functions , and I and others have so in the past somewhere.

But the main thing is my method is designed for analytic continuation.

The problem he gave was at a point that was not even continu.

So I see that as a somewhat violation of conditions although I did not clearly stated the conditions.
Without the alternating part that problem probably goes away , even if we hit a natural boundary ...

Well analytic at the boundary is usually hard to show, unless we get some *good* recursion and induction.
But still many mysteries about them.

regards

tommy1729