It can still make sense if you consider the zero's for every truncated sum.
So zero's outside analytic continuation can make sense.
And a summability method for that integral might help.
I remember as a kid , I somewhat rediscovered the Riemann Hypothesis.
I was looking for zero's of the zeta function , being aware it had a pole.
At that time I did not know complex analysis or even got officially introduced to complex numbers.
I also missed the whole number theory thing.
So i just wanted to find zero's of a function that looked nice, without knowing analytic continuation , calculus , formal complex numbers or number theory.
And I did.
With the truncated sum for the zeta and some more tricks I rediscovered that the zero's were on the critical line.
The intuition I had was that every function apart from of the form exp(..) and gamma(..) had a zero.
This probably followed from rediscovering of the complex numbers.
Therefore I said all those functions had zero's.
I considered a function were the zero was hard to find and the function easy to define.
so ended with zeta.
probably inspired by exp because they did not have a 0.
So I tested my ideas and found critical zero's with 123lotus or whatever that predeccessor of excel was called.
I did not tell anyone because I thought I had something new and special lol.
regards
tommy1729
So zero's outside analytic continuation can make sense.
And a summability method for that integral might help.
I remember as a kid , I somewhat rediscovered the Riemann Hypothesis.
I was looking for zero's of the zeta function , being aware it had a pole.
At that time I did not know complex analysis or even got officially introduced to complex numbers.
I also missed the whole number theory thing.
So i just wanted to find zero's of a function that looked nice, without knowing analytic continuation , calculus , formal complex numbers or number theory.
And I did.
With the truncated sum for the zeta and some more tricks I rediscovered that the zero's were on the critical line.
The intuition I had was that every function apart from of the form exp(..) and gamma(..) had a zero.
This probably followed from rediscovering of the complex numbers.
Therefore I said all those functions had zero's.
I considered a function were the zero was hard to find and the function easy to define.
so ended with zeta.
probably inspired by exp because they did not have a 0.
So I tested my ideas and found critical zero's with 123lotus or whatever that predeccessor of excel was called.
I did not tell anyone because I thought I had something new and special lol.
regards
tommy1729