Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Continuum sums -- a big problem and some interesting observations
#3
Yeah, that part wasn't right. What I meant was Fourier expansions of periodic approximations, like taking this:



(a periodic approximation function for the given function)

which has imaginary period , then expand it either as a Fourier series along a line like , which is to the "right" of the singularity (or singularities when dealing with the approximations), or expand it along one like , 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.
Reply


Messages In This Thread
RE: Continuum sums -- a big problem and some interesting observations - by mike3 - 10/06/2010, 03:34 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Interesting commutative hyperoperators ? tommy1729 0 368 02/17/2020, 11:07 PM
Last Post: tommy1729
  Very interesting topic Ansus 0 759 10/01/2019, 08:14 PM
Last Post: Ansus
  THE problem with dynamics tommy1729 1 2,830 04/04/2017, 10:52 PM
Last Post: tommy1729
  [sci.math] halting problem skeptic. tommy1729 0 1,957 05/30/2015, 09:24 PM
Last Post: tommy1729
  2015 Continuum sum conjecture tommy1729 3 4,031 05/26/2015, 12:24 PM
Last Post: tommy1729
  Problem with cauchy method ? tommy1729 0 2,179 02/16/2015, 01:51 AM
Last Post: tommy1729
  Another way to continuum sum! JmsNxn 6 7,495 06/06/2014, 05:09 PM
Last Post: MphLee
  Further observations on fractional calc solution to tetration JmsNxn 13 16,022 06/05/2014, 08:54 PM
Last Post: tommy1729
  Remark on Gottfried's "problem with an infinite product" power tower variation tommy1729 4 6,028 05/06/2014, 09:47 PM
Last Post: tommy1729
  On naturally occuring sums tommy1729 0 2,196 10/24/2013, 12:27 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)