Fourier series (2 same functions different inequality signs)

[izen]

Homework Statement

these two functions will give the same Fourier series? because when I write the graph they look the same?

Homework Equations

The Attempt at a Solution

in the picture

thank you

 

[jbunniii]

The series coefficients are defined by an integral. If you change the value of a function at a finite number of points, can the integral give you a different result?

 

[izen]

The series coefficients are defined by an integral. If you change the value of a function at a finite number of points, can the integral give you a different result?

I think integral give a different result so they are different ? not 100% sure

because in my lecture note all the example are < ,> there is no single example has <=, >=. so when I tried to do some exercise there are <=, >= on the functions so it kinda confused me. please explain more

 

[jbunniii]

I think integral give a different result so they are different ? not 100% sure

No, you can change a function at a finite number of points, and the integral will still be the same. So your Fourier coefficients will be the same for both functions.

 

[izen]

No, you can change a function at a finite number of points, and the integral will still be the same. So your Fourier coefficients will be the same for both functions.

thank you