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RE: RE: Problem with Sum

• To: mathgroup at smc.vnet.net
• Subject: [mg44056] RE: RE: Problem with Sum
• From: "Sung Jin Kim" <kimsj at mobile.snu.ac.kr>
• Date: Sun, 19 Oct 2003 01:11:07 -0400 (EDT)
• Reply-to: <kimsj at mobile.snu.ac.kr>
• Sender: owner-wri-mathgroup at wolfram.com

> -----Original Message-----
> From: Andrzej Kozlowski [mailto:akoz at mimuw.edu.pl]
To: mathgroup at smc.vnet.net
> Sent: Saturday, October 18, 2003 4:13 PM
> In[1]:=
> Sum[(-1)^m*(DiscreteDelta[1 - 2*m] -
>      2*DiscreteDelta[3*m + 1]), {m, -Infinity, Infinity}]
> 
> Out[1]=
> I + 2*(-1)^(2/3)
> as meaning the same as:
> 
> In[2]:=
> Integrate[(-1)^x*(DiracDelta[x - 1/2] -
>      2*DiracDelta[x + 1/3]), {x, -Infinity, Infinity}]
> 
> Out[2]=
> I + 2*(-1)^(2/3)

In my test, I got exact results which both of you denoted as bellow:
In[1]:= Sum[(-1)^m * (DiscreteDelta[1 - 2*m] - 2*DiscreteDelta[1 +
3*m]),{m, -Infinity, Infinity}]
Out[1]:= I + 2*(-1)^(2/3)
In[2]:= Sum[(-1)^m*(DiscreteDelta[1 - 2*m] - 2*DiscreteDelta[1 + 3*m]),
{m, 10, 10}]
Out[2]:= 0
In[3]:= Integrate[(-1)^x*(DiracDelta[x - 1/2] -2*DiracDelta[x + 1/3]),
{x, -Infinity, Infinity}]
Out[3]:= I + 2*(-1)^(2/3)

However, I am not easy to catch the meaning of these similarity between
In[1] and In[2]. Andrzej, do you mean that both are mathematically
equivalent or especially equivalent in Mathematica? I try to ask this to
you because I have some memory to study such a similar concept in my
student period.

> Andrzej Kozlowski
> Yokohama, Japan
> http://www.mimuw.edu.pl/~akoz/
> http://platon.c.u-tokyo.ac.jp/andrzej/