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Re: Are elliptic functions orthogonal?
Posted:
Jan 20, 2013 11:50 PM


On Jan 20, 10:04 pm, h...@work.pk (Sycho) wrote: > This just in to the alt.2600 news room. On Sun, 20 Jan 2013 17:22:01 > 0800 (PST) it was announced to all in a public briefing, Vaughan > Anderson <vaughan.andur...@gmail.com> made the following declaration > and shocked the world when the following was announced: > > > > > > > > > > >On Jan 18, 10:28 pm, h...@work.pk (Sycho) wrote: > >> This just in to the alt.2600 news room. On Fri, 18 Jan 2013 14:58:51 > >> 0800 (PST) it was announced to all in a public briefing, Jeremy > >> Sample <vaughan.andur...@gmail.com> made the following declaration and > >> shocked the world when the following was announced: > > >> >Can an arbitrary function be uniquely expanded in a series solution of > >> >elliptic integrals? > > >> >That is to say, can you apply an algorithm like the Fourier analysis, > >> >(or Bessel, Legendre, etc.) to an arbitrary function, using elliptic > >> >integrals instead of trigonometrics as the basis function? > > >> >I wonder if this could be a useful technique for reducing nonlinear > >> >data, in systems where certain, simple cases are known to have > >> >elliptic solutions. > > >> >Your scholarly input would be greatly appreciated, even if it means > >> >referring me to journal articles, as long as they're by specific > >> >authors. > > >> >TIA. > > >> They can be whatever you want them to be so long as you pay them > >> enough "hush" money. > > >> Cookies also help. > > >What is it with you and cookies? The holidays are over, and it's time > >to start on your New Year's resolution to lose weight. ;) > > The dark side *always* has cookies. It's an unwritten law. > > >I believe that elliptic integrals (or functions), in general, are not > >orthogonal, and therefore not suitable for use in series expansions. > >But since they are not a discretely indexed function like Trigs, > >Bessels, Legendres, etc. it may be possible to *find* values for the > >elliptic control parameter that make them orthogonal, which would > >impose a discrete index onto the functions. > > Everybody's got to believe in something. I, OTOH believe I'll have > another beer. > > >There would be a continuum of families of these discretely indexed > >elliptics. Also, the orthogonalization would have to be performed in > >two dimensions, since elliptics are doubly periodic. If I'm lucky, > >and this works, it would be a newly discovered kind of elliptic, and > >it could advance the solution to a highly nonlinear, noncrypto > >problem I'm working on. It might be enough to turn into a > >dissertation, to finally wrap up the ol' PhD. > > >I gotta find the time to crunch the numbers. Wish me luck. > > Don't crunch numbers. Crunch cookies because they're tastier. > > HAIL FLUFFY!!1!! >  > If monsters ever sat around the campfire telling ghost stories, do you > think it would start like this.. "It was a bright and sunny day..."
Exactly what do you mean by "cookie"?



