# Fourier Cosine series of cos(x)

• Oct 14th 2006, 12:48 AM
sarahisme
Fourier Cosine series of cos(x)
Hello peoples,

I think this is a trick question... well sort of :P

http://img133.imageshack.us/img133/472/picture8ox1.png

for part (a) i get that the cosine Fourier Series for f(x) = cos(x) to be:

http://img138.imageshack.us/img138/6114/picture9sq2.png

i hope that is ok, but its part (b) that is troubling me...

is all that happens as http://img138.imageshack.us/img138/7...cture10gf7.png is that the cosine Fourier series of cos(x) goes to 0?

i am guessing i am missing some trick to this question?

Cheers! :D

Sarah
• Oct 14th 2006, 03:40 AM
CaptainBlack
Quote:

Originally Posted by sarahisme
Hello peoples,

I think this is a trick question... well sort of :P

http://img133.imageshack.us/img133/472/picture8ox1.png

for part (a) i get that the cosine Fourier Series for f(x) = cos(x) to be:

http://img138.imageshack.us/img138/6114/picture9sq2.png

i hope that is ok, but its part (b) that is troubling me...

is all that happens as http://img138.imageshack.us/img138/7...cture10gf7.png is that the cosine Fourier series of cos(x) goes to 0?

i am guessing i am missing some trick to this question?

Cheers! :D

Sarah

Look at the limit of the coefficient of cos(pi x /alpha) as alpha goes to
pi.

You should find that the limit as alpha goes to pi of all the coeficients
other than that of cos(pi x /alpha) are 0, while that of cos(pi x /alpha)
is 1.

RonL
• Oct 14th 2006, 03:42 PM
sarahisme
Quote:

Originally Posted by CaptainBlack
Look at the limit of the coefficient of cos(pi x /alpha) as alpha goes to
pi.

You should find that the limit as alpha goes to pi of all the coeficients
other than that of cos(pi x /alpha) are 0, while that of cos(pi x /alpha)
is 1.

RonL

i yep i see, i need to be more careful with the n = 1 term when alpha = pi.

thanks for the help! :D