Now hold on a minute.
If I am not mistaken you took micks function and provided an alternative series expansion that converges in a larger domain.
But now you use the alternative series expansion and plug in 1/2 instead of 2.
But if you took the original series for mick's function it converges better if you pick 1/2 instead of 2.
So you got this one backwards ?
You only needed to replace 2 with 1/2 in micks original series, and that converges.
So if you do nothing or go backwards from your alternative series to the double sum , back to micks definition , then your problem is solved.
Then it looks like one of your simple "plug-ins".
Or did I make a mistake ?
The idea of using geometric series seems to work so often , apart from anyting that resembles ( with multiple sums , internal or external )
1+1+1+1+...
which means here that 1/2 and 2 work but 1 does not extend ?
Just an idea or the philosophy of the geometric series in my viewpoint.
regards
tommy1729
If I am not mistaken you took micks function and provided an alternative series expansion that converges in a larger domain.
But now you use the alternative series expansion and plug in 1/2 instead of 2.
But if you took the original series for mick's function it converges better if you pick 1/2 instead of 2.
So you got this one backwards ?
You only needed to replace 2 with 1/2 in micks original series, and that converges.
So if you do nothing or go backwards from your alternative series to the double sum , back to micks definition , then your problem is solved.
Then it looks like one of your simple "plug-ins".
Or did I make a mistake ?
The idea of using geometric series seems to work so often , apart from anyting that resembles ( with multiple sums , internal or external )
1+1+1+1+...
which means here that 1/2 and 2 work but 1 does not extend ?
Just an idea or the philosophy of the geometric series in my viewpoint.
regards
tommy1729