Problems with a symbolic sum

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1980] Problems with a symbolic sum
• From: tlm at ameslab.gov (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

math
Mathematica 2.2 for NeXT
-- 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.

Tom
--
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 ameslab.gov

Executive Director:  Undergraduate Computational Engineering and Sciences
http://uces.ameslab.gov/uces/home.html

```

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