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MathGroup Archive 2006

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg64342] Re: Delta function could not be got when delta function is the answer
  • From: albert <awnl at arcor.de>
  • Date: Sun, 12 Feb 2006 04:00:28 -0500 (EST)
  • References: <dsk8cn$i6d$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

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. 

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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