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 Continuum sums -- a big problem and some interesting observations Ansus Junior Fellow Posts: 20 Threads: 5 Joined: Aug 2008 10/09/2010, 05:46 PM (This post was last modified: 10/17/2010, 12:17 PM by Ansus.) (10/05/2010, 11:40 AM)mike3 Wrote: I mean it's not something weird like $\psi(z + 1) + e^e \sin(2\pi z) + e^{\sin(4\pi z)}$ or something contrived and wobbly and all that (yes, I know these aren't rigorous terms.). Instead, it's just: $\sum_z \frac{1}{z + 1} = \psi(-z)$. And note also that $\psi(-z)=\psi(z + 1)+\pi \cot(\pi z)$ so the both solutions only differ by a periodic function (which can be filtered out on each continous range separately in the process of finding the natural value by requiring monotonous derivatives of higher order for example). « Next Oldest | Next Newest »

 Messages In This Thread Continuum sums -- a big problem and some interesting observations - by mike3 - 10/05/2010, 11:40 AM RE: Continuum sums -- a big problem and some interesting observations - by tommy1729 - 10/05/2010, 11:33 PM RE: Continuum sums -- a big problem and some interesting observations - by mike3 - 10/06/2010, 03:34 AM RE: Continuum sums -- a big problem and some interesting observations - by tommy1729 - 10/06/2010, 12:44 PM RE: Continuum sums -- a big problem and some interesting observations - by mike3 - 10/07/2010, 04:32 AM RE: Continuum sums -- a big problem and some interesting observations - by Ansus - 10/09/2010, 03:13 PM RE: Continuum sums -- a big problem and some interesting observations - by mike3 - 10/10/2010, 12:58 AM RE: Continuum sums -- a big problem and some interesting observations - by Ansus - 10/09/2010, 05:46 PM RE: Continuum sums -- a big problem and some interesting observations - by Ansus - 10/10/2010, 05:31 AM RE: Continuum sums -- a big problem and some interesting observations - by Ansus - 10/10/2010, 06:06 AM RE: Continuum sums -- a big problem and some interesting observations - by Ansus - 10/10/2010, 08:02 AM RE: Continuum sums -- a big problem and some interesting observations - by mike3 - 10/11/2010, 10:36 AM RE: Continuum sums -- a big problem and some interesting observations - by Ansus - 10/11/2010, 11:33 AM RE: Continuum sums -- a big problem and some interesting observations - by mike3 - 10/11/2010, 11:46 PM RE: Continuum sums -- a big problem and some interesting observations - by Ansus - 10/12/2010, 04:41 AM RE: Continuum sums -- a big problem and some interesting observations - by mike3 - 10/12/2010, 06:44 AM RE: Continuum sums -- a big problem and some interesting observations - by mike3 - 10/12/2010, 06:45 AM RE: Continuum sums -- a big problem and some interesting observations - by Ansus - 10/12/2010, 10:41 AM

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