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Topic: Help with finding zeros
Replies: 7   Last Post: Sep 14, 2010 3:35 PM

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Bob Adams

Posts: 55
Registered: 12/13/04
Re: Help with finding zeros
Posted: Sep 13, 2010 11:37 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Sep 13, 10:01 am, "Rod" <rodrodrod...@hotmail.com> wrote:
> "Greg Neill" <gneil...@MOVEsympatico.ca> wrote in message
> news:BUpjo.55715$iw4.28826@unlimited.newshosting.com...

> > Robert Adams wrote:
> >> I could use a little help trying to solve the following engineering
> >> problem (no, I am not a student looking for homework help!)

> >> I need to find the values of w which cause the following summation to
> >> go to zero

> >> sum (n = 1 to N) of exp(-i*w*ln(n))
> >> where i is the usual sqrt(-1)
> >> For a given N, there are infintely many solutions due to the
> >> periodicity of exp(-i ...)
> >> How do I find these solutions?

> >> Thanks for any pointers.
> >> Bob Adams
> > Have you looked into expanding the exponentials into
> > trig form?  You'll then have a sum of cos and
> > imaginary sin terms which will each have to sum to
> > zero separately.

> That's my approach as well
> Wouldn't w have to be complex to achieve both series being zero.
> Is this not a truncated zeta function?- Hide quoted text -
> - Show quoted text -

Yes, this is related to the zeta function.

I was hoping to to find a solution where w is real, but this may not
be possible as you point out


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