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 Continuum sums -- a big problem and some interesting observations mike3 Long Time Fellow Posts: 368 Threads: 44 Joined: Sep 2009 10/06/2010, 03:34 AM (This post was last modified: 10/06/2010, 03:35 AM by mike3.) Yeah, that part wasn't right. What I meant was Fourier expansions of periodic approximations, like taking this: $f_u(z) = \frac{1}{1 + \left(u \sinh\left(\frac{z}{u}\right)\right)},\ u \in \mathbb{R}$ (a periodic approximation function for the given function) which has imaginary period $2\pi i u$, then expand it either as a Fourier series along a line like $\Re(z) = 0$, which is to the "right" of the singularity (or singularities when dealing with the approximations), or expand it along one like $\Re(z) = -2$, which is to the "left", then continuum-sum one of those Fourier series and take the limit at infinite period. When the resulting functions are analytically continued by the continuum-sum recurrence equations to the whole plane, they should yield continuum sums with singularities going to the left and right, respectively. « 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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