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From: Alberto on 9 Apr 2010 08:05
Hello everybody,

I am trying to compute using Matlab an expression of the sort
sum(n from 0 to infinity) Fn sin(n theta).
In this expression Fn should be a coefficient which is a function of n and I would like to find the expression for the generic coefficient.

I will probably have 4 equations with 4 coefficients, like F1n, F2n, F3n, F4n .
If I was in numerical Matlab the coefficients would be F1(n). F2(n)....etc...


I thought maybe someone had to represent Fourier coefficients or something like that.


I have two questions:
- how do i represent infinite sums ?
- how do i explicit the dependence of the terms from n ?

Thanks in advance

Alberto
From: Walter Roberson on 13 Apr 2010 00:02
Alberto wrote:

> I am trying to compute using Matlab an expression of the sort sum(n from
> 0 to infinity) Fn sin(n theta).
> In this expression Fn should be a coefficient which is a function of n
> and I would like to find the expression for the generic coefficient.

I gather that you are doing this symbolically.


> I will probably have 4 equations with 4 coefficients, like F1n, F2n,
> F3n, F4n .
> If I was in numerical Matlab the coefficients would be F1(n).
> F2(n)....etc...

> I thought maybe someone had to represent Fourier coefficients or
> something like that.

> I have two questions:
> - how do i represent infinite sums ?
> - how do i explicit the dependence of the terms from n ?

In maple, you would start with something like:

F1 := proc(n) binomial(n,3) end proc;

where binomial(n,3) is just a sample function to satisfy your statement
that "Fn should be a coefficient which is a function of n".

The syntax for MuPad procs is slightly different... e.g., I think it
might be end<underscore>proc instead of end<space>proc.

Once that is defined, then in Maple you would use

S1 := sum(F1(n)*sin(n*theta), n=0..infinity);

In Matlab with MuPad I do not know if that would work directly or if you
would have to use symsum() or a similar function name. Shouldn't take
more than a few seconds to find the right procedure name.

This particular example would result in

S1 := -((1/2)*I)*exp(I*theta)*(exp(I*theta)+1)/(exp(I*theta)-1)^3;

as it happens to be a form that Maple knows a closed-form solution to.

It doesn't take much to find a form that there is no known closed-form
solution to... for example, F1(n) being n!/exp(n) .
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