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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
>
>
>
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