Art Kalb

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13 years, 318 days

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These are replies submitted by Art Kalb

Hi,

 

I have been trying that to no avail. I keep getting output that is 540 pt  wide. Even when I get the width to scale up relative to the height, it is at the expense of the height. The width is always 540 pt.

Are you running Maple 12 or 11?

Regards.

 

 

I'm trying to compute.

I'm trying to compute.

It looks equivalent to what I wanted.

 

It looks equivalent to what I wanted.

 

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
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