Can 1/a Be Expanded Using Fourier Expansion?

[kaizen.moto]

Dear all,

Iam just wondering whether the term 1/a can be expanded using Fourier expansion. If it does, please let me know how to to do this.

Thank for any kind help.

 

[HallsofIvy]

What do you mean bu "the term 1/a"? Normally, we expand functions in Fourier series, not numbers. Of course, we can think of f(z)= 1/a as the constant function. In that case, the Fourier series is simply (1/a)+ 0 sin(z)+ 0 cos(z)+ ...

If you mean f(z)= 1/z, then, yes, you can find a Fourier series for 1/z using the standard formulas. It will not converge at z= 0, of course.

 

[kaizen.moto]

How about f(x) = (1 - x/a), what would be the solution after Fourier expansion?

 

[LCKurtz]

Any constant is a finite Fourier series with all the sine and cosine terms having 0 coeifficients. There is nothing to calculate.

 

[LCKurtz]

How about f(x) = (1 - x/a), what would be the solution after Fourier expansion?

Your f(x) needs to be periodic to have a FS.

 

[Mark44]

Moderator's note: I copied several posts from the thread that was started in the Mathematics technical section.