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/