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- Helping hand
- 2012-12-16 01:08:16
Did you use Euler's definition that the zeta of 2n is equal to Bernoulli of 2n times 2pi to the 2n over 2 times 2n factorial times minus 1 to the n+1th power?
If you did then it did not work because it only works for non-zero positive even integers because the Bernoulli of 0 can either be -1/2 or 1/2
- Alex23
- 2012-02-06 07:57:22
That is a big statement. Are you sure 4 is correct?
That is a celebrated result and nowhere did I read it is an indeterminate series, but that it just converges to Euler's result.
- Stangerzv
- 2012-02-05 22:12:04
To others, infinity is a concept not a number but to me there is even and odd infinity. To them 1+infinity=infinity but to me 1+infinity>infinity. They got all those values like 1/12 or etc because they play with the infinity as they like. If you have a function of 1-1+1-1+1..infinity, if you use their concept you would get sometimes S=1/2 yet you know when it is even, S=0 and when it is odd, S=1 and this function alternates 0 & 1 to the infinity. I think people need to respect the infinity, otherwise we would be hay-wired. I do sometimes play with the infinity and I can proof that Zeta function
is not always true and converge to value 4.- bobbym
- 2012-02-03 06:32:13
Hi Alex23;
That is something I can not answer. I only have the tiniest bit of understanding of that page. Not enough to even comment.
- Alex23
- 2012-02-03 06:27:48
I read the article. So the definition changes for that domain with gamma functions and what not.
Thanks for clearing up the definition does not hold for Re(s) < 1. In other forums people were just stating it is an unexpected result and we have to live with it and I was thinking WHAT??!, the equality is altogether wrong, meaning the sum over ones.
My question is how analytic continuation does not address a new function all together? Is it because the transformation is unique; that is the key?
Cheers!
- bobbym
- 2012-02-01 05:45:59
Hi Alex23;
Welcome to the forum!
The zeta function is defined like this
only when the sum converges which it clearly does not for s=0. So the above definition does not hold. Look here for how an analytic continuation is used:
http://mathworld.wolfram.com/RiemannZetaFunction.html
- Alex23
- 2012-02-01 03:42:08
Alright, ζ(0) = 1 + 1 + 1 + ... = -1/2. Miracles do happen!
I want to comprehend what this means but it seems to me this just supersedes quantitative math.
Is there supposed to be a qualitative limited meaning to it?
Because if you forget the outcome is from zeta and just write 1 + 1 + 1 + ... = -1/2 this clearly is nonsense alone like that, as Hardy and Littlewood thought initially of it mailed by Ramanujan.
Math gurus enlighten me. 