Re: Re: Delta function could not be got when delta function is the answer

*To*: mathgroup at smc.vnet.net*Subject*: [mg64351] Re: [mg64342] Re: Delta function could not be got when delta function is the answer*From*: Pratik Desai <pdesai1 at umbc.edu>*Date*: Mon, 13 Feb 2006 03:15:12 -0500 (EST)*References*: <dsk8cn$i6d$1@smc.vnet.net> <200602120900.EAA13299@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

albert wrote: >PengYu.UT at gmail.com wrote: > > > >>Sum[E^(-2*Pi*I*n*p*k), {n, -Infinity, Infinity}] >> >>The above summation should give an delta function. >> >> > >which is no function but a distribution (or generalized function)... > > > >>However, 0 is given >> >> > >which is correct for almost every p and k :-) > > > >>by Mathematica 5.0. Is it a bug. >> >> > > > Check out the site http://functions.wolfram.com/GeneralizedFunctions/DiracDelta/ and you can download a notebook with all kinds of info about DiracDelta, among which is this DiracDelta[x] == Sum[HoldForm[E^(I*k*x)], {k, -Infinity, Infinity}]/(2*Pi) /; -2*Pi < x < 2*Pi I added the holdform because mathematica automatically evaluates the sum to zero, I tried to use 2.5.2 Manipulating Sets of Transformation Rules of m-book but was not able to apply the transformation?? Hope this helps Pratik >depends on what you expect that mathematica can do. As far as I know, it can >handle the delta function only to some extend in some functions like >Integrate but does not claim to support distributions in general (see >documentation for DiracDelta and 'Generalized Functions'). But maybe I am >wrong here, I personally wouldn't expect mathematica to do too much useful >stuff with DiracDelta especially if it is not in the realm of D, Integrate >and FourierTransform... > > > >>Is there any workaround to get the delta function? >> >> > >from the sum you used as input: I don't know. >if input doesn't matter try these :-): > D[UnitStep[x], x] > FourierTransform[1/Sqrt[2 Pi], k, x] > >hth, > >albert > > >

**References**:**Re: Delta function could not be got when delta function is the answer***From:*albert <awnl@arcor.de>