Re: sum R

On Wed, 16 Apr 2008 11:58:48 EDT, amy666 <tommy1729@xxxxxxxxxxx>
wrote:

david wrote :

On Wed, 16 Apr 2008 07:59:45 EDT, amy666
<tommy1729@xxxxxxxxxxx>
wrote:

taking the sum over the reals in a real interval.

i would like to read more about it on the internet.

in general for the interval (0,1) with bounded range
(-1,1) the sum over the reals converges if the
integral over (0,1) is 0.

Nonsense. Would you like to show us the proof of
this, or should we
start with a counterexample?

it does not always hold.

Right. So when you said "in general..." you were speaking
nonsense.

depends on the amount of non-differentiable points.

if f(x) is smooth it does and both = 0.

Oh my god. Yes, this is true, because the sum of an arbitrary
collection of 0's is 0.

You're really so proud of realizing that the sum of 0's is 0
that you needed to post this?

what the integral does is say what the average is for the subset of measure 1.



i denote "[sum R f(x)]0_1 "

understanding gibbs phenomenon is sufficient for the
sum over the reals of a fourrier series.

Huh? What does that mean, exactly?

basicly that the sum over all the reals in the interval (0,1) for an f(x) with f(x) a fourrier series is not hard to compute.

Jesus. That sum for a fourier series does not exist, except when the
series is identically zero. This has nothing to do with Gibbs.


what is intresting is the analytic computation of
the sums over the reals if convergeant.

Huh? If it exists, the sum over the reals of a
function is a _number_,
not a function. You really think that, for example,
analytic
continuation of 0 or analytic continuation of 42 is
"interesting"?

COMPUTATION not CONTINUATION.

Yes, I misread what you wrote, sorry.

you are confusing those 2.

simpler said , giving a closed form for those numbers.

Why in the world do you think this is "interesting"?

First, you haven't given any examples where the sum
converges, _except_ in the case where f(t) = 0 for
all t.

And second, of course there _are_ cases where the sum
converges. But that happens only when f vanishes except
at countably many points, and in that case what you have
is just an ordinary sum. There's no difference whatever
between calculating your amazing sum_R things and
calculating the sum of an arbitrary series.

in much the same way we solve definite integrals.

like gamma(1/2) = sqrt(pi) and similar.



and also if a summability method is possible in case
of divergeance.

i would like to read more about it on the internet.

does anyone know a good website for it ?

You should set up your own. Then you wouldn't have to
worry about
whether you were making any sense - you could just
post your
marvelous insights and then come back and read them.

and maybe i should add that computation is not the same as continuation for people like you :)

Yup. Before or after you point out that your fascinating point of view
shows that 0 + 0 + ... = 0.


regards

tommy1729

David C. Ullrich

regards
tommy1729

David C. Ullrich
.

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