Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2005
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2005

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Gaussian sums (Was: Speeding up simple Mathematica expressions?)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg63330] Re: Gaussian sums (Was: Speeding up simple Mathematica expressions?)
  • From: AES <siegman at stanford.edu>
  • Date: Sat, 24 Dec 2005 07:18:55 -0500 (EST)
  • Organization: Stanford University
  • References: <do8ioc$rvd$1@smc.vnet.net> <dodec4$65o$1@smc.vnet.net> <dogju0$pnl$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <dogju0$pnl$1 at smc.vnet.net>,
 Paul Abbott <paul at physics.uwa.edu.au> wrote:

> > A colleague Adnah Kostenbauder has pointed out that this seems to be a 
> > version of "Jacobi's imaginary transformation" given in Section 21.51 of 
> > Whittaker and Watson.  Presumably it also has a connection to some 
> > obscure property of the EllipticTheta functions.
> 
> Not an obscure property. It is a basic transformation. See
> 
>   http://functions.wolfram.com/09.03.16.0001.01

   Working definition of "obscure" = "Something I don't know"
   (but that Paul and David Lichtbau generally do)

> > In physical terms f corresponds an array of narrow, parallel, 
> > transversely but equally displaced gaussian beams with gaussianly 
> > decreasing amplitude across the array; g represents a set of wider, 
> > increasingly tilted gaussian beams all convering onto a common spot; and 
> > h has the appearance of an array of wide, nominally parallel gaussian 
> > beams with equal but imaginary-valued transverse displacements.
> 
> Most interesting.

   I'll post some illustrations of the optical beam embodiments
   on my web page eventually -- but it may take a little while.


  • Prev by Date: Puzzle Challenge
  • Next by Date: Re: Matrices with Mathematica 5.1
  • Previous by thread: Re: Gaussian sums (Was: Speeding up simple Mathematica expressions?)
  • Next by thread: Extracting information from lists