Art Kalb

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16 years, 207 days

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I was looking for a closed form expression.

 

 

I was looking for a closed form expression.

 

 

Hi.

Here is an example of what I am trying to do (a fourier series):

test := `assuming`([int((cos((2*Pi*6)*t/T)+t^2)*cos(2*Pi*n*t/T), t = -(1/2)*T .. (1/2)*T)], [T > 0]);

The result of this is:

1/4*T*(Pi^2*n^4*sin(Pi*n)*T^2+4*Pi^2*n^4*sin(Pi*n)+72*sin(Pi*n)*T^2-2*n^2*sin(Pi*n)*T^2+2*Pi*n^3*cos(Pi*n)*T^2-36*Pi^2*n^2*sin(Pi*n)*T^2-72*Pi*n*cos(Pi*n)*T^2)/Pi^3/n^3/(-36+n^2)

I then form the fourier series sum of these coefficients from 1 to N.

The coefficients are composed of two parts:

cos(2*Pi*t*t/T)  and  1/2*(-1)^n/n^2/Pi^2*T^3

I would like to write the fourier sum in the following form:

f(6) + sum of g(n) from 1 to N excluding 6

It's this second part I am having trouble generating when I don't want to specify N up front.

 

Art

 

 

Hi.

Here is an example of what I am trying to do (a fourier series):

test := `assuming`([int((cos((2*Pi*6)*t/T)+t^2)*cos(2*Pi*n*t/T), t = -(1/2)*T .. (1/2)*T)], [T > 0]);

The result of this is:

1/4*T*(Pi^2*n^4*sin(Pi*n)*T^2+4*Pi^2*n^4*sin(Pi*n)+72*sin(Pi*n)*T^2-2*n^2*sin(Pi*n)*T^2+2*Pi*n^3*cos(Pi*n)*T^2-36*Pi^2*n^2*sin(Pi*n)*T^2-72*Pi*n*cos(Pi*n)*T^2)/Pi^3/n^3/(-36+n^2)

I then form the fourier series sum of these coefficients from 1 to N.

The coefficients are composed of two parts:

cos(2*Pi*t*t/T)  and  1/2*(-1)^n/n^2/Pi^2*T^3

I would like to write the fourier sum in the following form:

f(6) + sum of g(n) from 1 to N excluding 6

It's this second part I am having trouble generating when I don't want to specify N up front.

 

Art

 

 

Hi,

This does not work if N is not bound to a number.

add(n,n=select(isprime,[$1..N])) generates an error

add(n,n=select(isprime([$1..10])) is o.k.

 

I would like something like the first option. Conversion of the add command to a sum is an invalid form for sum.

 

Any ideas?

 

 

 

Hi,

This does not work if N is not bound to a number.

add(n,n=select(isprime,[$1..N])) generates an error

add(n,n=select(isprime([$1..10])) is o.k.

 

I would like something like the first option. Conversion of the add command to a sum is an invalid form for sum.

 

Any ideas?

 

 

 

Hi,

 

Thanks for the reply. What you are doing is not quite what I had in mind. I am looking to sum over the integers minus a finite set, not sum the integers minus a certain. Specifically, I am trying to write a procedure that will sum terms that do not have removable singularities separately from the terms that do have removable singularities.

An example...

b[n]=2*sin(Pi*n)/(Pi*(n^2-1))     (yes, this is a fourier series...)

The above coefficients over n (positive integer <= N) have a removable singularity at n=1. I would like write the fourier series as the addition of the removable terms plus the rest of the terms. In many cases, all the coefficients of terms without singularities will be zero.

I hope this clarifies things a bit.

 

Art

Hi,

 

Thanks for the reply. What you are doing is not quite what I had in mind. I am looking to sum over the integers minus a finite set, not sum the integers minus a certain. Specifically, I am trying to write a procedure that will sum terms that do not have removable singularities separately from the terms that do have removable singularities.

An example...

b[n]=2*sin(Pi*n)/(Pi*(n^2-1))     (yes, this is a fourier series...)

The above coefficients over n (positive integer <= N) have a removable singularity at n=1. I would like write the fourier series as the addition of the removable terms plus the rest of the terms. In many cases, all the coefficients of terms without singularities will be zero.

I hope this clarifies things a bit.

 

Art

Hi,

 

I guess I should have included the caveat of 3D. I was aware of this package, but it doesn't appear to do three-dimensional problems.

 

Regards.

 

Hi, Thanks Art
Hi, Thanks Art
Hi, Thanks for the input. I was really looking for a way to do this when N is indeterminate. I didn't say N was indeterminate, sorry. Any suggestions? Art
Hi, Thanks for the input. I was really looking for a way to do this when N is indeterminate. I didn't say N was indeterminate, sorry. Any suggestions? Art
Hi, Thanks for the clarification. Regards, Art
Hi, Thanks for the clarification. Regards, Art
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