Re: Can't reproduce a solution found in a paper using Mathematica
- To: mathgroup at smc.vnet.net
- Subject: [mg102890] Re: Can't reproduce a solution found in a paper using Mathematica
- From: dr DanW <dmaxwarren at gmail.com>
- Date: Tue, 1 Sep 2009 03:54:18 -0400 (EDT)
- References: <h7diuh$kbc$1@smc.vnet.net>
First, do not use square brackets [] as grouping structures in
Mathematica. Square brackets have a specific meaning in Mathematica,
and are only used for function calls. Always use parentheses for
grouping in Mathematica.
Once that is cleared up, look at your expression. You have an
infinite sum inside an integral. Mathematica will try to evaluate
that infinite sum. It will work really, really hard on this. Of
course, you already know that you do not care what the sum is, since
your solution is in terms of an infinite sum. What you are really
looking for is the integral of each term.
So, integrate term-by term. Your mth term is easily handled by
Mathematica:
In[]: Integrate[(Cosh[((2*m + 1)*Pi*y)/a]*Sin[((2*m + 1)*Pi*x)/a])/
(Cosh[((2*m + 1)*Pi*b)/a]*(2*m + 1)^3), {y, 0, b}, {x, 0, a}]
Out[]: (2*a^2*Cos[m*Pi]^2*Tanh[(b*(1 + 2*m)*Pi)/a])/((1 + 2*m)^5*Pi^2)
Now you may be tempted to put your solution together in Mathematica,
but remember, you still have an infinite sum that Mathematica will
attempt to solve. Fortunately, it realizes pretty quickly that there
is no closed form solution and returns the sum unevaluated.
The lesson here is that Mathematica is not a substitute for pencil and
paper for doing math. It is a powerful supplement, but you have to
some of the work yourself, especially if you are looking for an
elegant expression.
Daniel