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Problems with a symbolic sum

  • To: mathgroup at
  • Subject: [mg1980] Problems with a symbolic sum
  • From: tlm at (Tom Marchioro)
  • Date: Mon, 4 Sep 1995 22:21:48 -0400
  • Organization: Iowa State University, Ames, Iowa

for one of our on-line computational science textbooks I was in the  
process of translating an example from Maple to Mathematica.   
Unfortunately, it appears that this is a case where Mma comes up short.   
To wit, Mma gives the following

Mathematica 2.2 for NeXT
Copyright 1988-93 Wolfram Research, Inc.
 -- NeXT graphics initialized -- 

In[1]:= Needs["Algebra`SymbolicSum`"];

In[2]:= Sum[(((2*i)/(2*n+1))*(1/n)/Sqrt[((2*i)/(2*n+1) 
-1/2)^2 + (1/2)^2]), {i, -n, n}]

Out[2]= 0

which is flat-out wrong.  Need the above sum *in Mathematica* in the limit  
as n-> Infinity, am open to suggestions as to how SymbolicSum can be  
coaxed into getting the right answer. Is it at least correct in the  
upcoming version of Mathematica?

Incidentally, the sum arises in the computation of the electrostatic  
potential from a continuous charge distribution on a wire. 

Thanks for any help which can be offered.

Dr. Thomas L. Marchioro II      Two-wheeled theoretical physicist
Applied Mathematical Sciences   515-294-9779
Ames Laboratory                 515-432-9142 (home)
Ames, Iowa 50011                tlm at

Executive Director:  Undergraduate Computational Engineering and Sciences

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