Re: FourierTransform of Sign^2 ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg80163] Re: FourierTransform of Sign^2 ?*From*: Hendrik van Hees <hees at comp.tamu.edu>*Date*: Tue, 14 Aug 2007 06:57:38 -0400 (EDT)*Organization*: Texas A&M University*References*: <f9p6c7$rvv$1@smc.vnet.net>

Dana DeLouis wrote: >> Mathematica (v. 5.0, Mac) gives >> -Sqrt[2 Pi]*DiracDelta[q] >> with a minus sign. > > There was a discussion in another group recently about 5.2 with something > similar. I'm not sure what the correct answer is, but I thought you might > find this interesting. > > equ = Sech[x*a]; > > 5.2 takes about 1 minute to do this... > > (* 5.2 *) > > Timing[FourierTransform[equ, x, s]] > > {55.594, > (Sqrt[Pi/2]*Sech[(Pi*s)/ (2*a)])/a} Again, to check against my ancient 4.0: Mathematica 4.0 for Students: Linux Version Copyright 1988-1999 Wolfram Research, Inc. -- Motif graphics initialized -- In[1]:= equ=Sech[x*a]; In[2]:= Timing[FourierTransform[equ, x, s]] Pi Pi s Sqrt[--] Sech[----] 2 2 a Out[2]= {1.82 Second, -------------------} a It seems that version 5.2 gives the same solution as 4.0, but takes longer. Perhaps we have to check whether 5.2 and 4.0 or 6.0 gives the correct answer by hand? -- Hendrik van Hees Texas A&M University Phone: +1 979/845-1411 Cyclotron Institute, MS-3366 Fax: +1 979/845-1899 College Station, TX 77843-3366 http://theory.gsi.de/~vanhees/faq mailto:hees at comp.tamu.edu