Sum of Fourier series

ronn · 2014-02-20 07:32:35

We have a 2pi-periodic even function for which

f(t) = 0 when 0 < t < pi-2
f(t) = pi when pi-2 < t <pi

The functions trigonometric Fourier series is

How can we decide the series sum for when

?

bobbym · 2014-02-20 12:10:56

Hi;

I already summed that series for all t. It involves the hypergeometric series and is quite complicated.

ronn · 2014-02-22 04:00:32

Can't Parseval's formula be used for this?

bobbym · 2014-02-22 04:07:51

What did you get using it?

ronn · 2014-02-22 07:37:34

I wrote wrong in the last post, it's supposed to be

Please help!!!

anonimnystefy · 2014-02-22 08:09:26

Hi ronn

M give the answer of

.

ronn · 2014-02-22 08:29:58

anonimnystefy wrote:

Hi ronn
M give the answer of
.

Could you PLEASE write HOW to solve the problem?

bobbym · 2014-02-22 13:54:01

Hi ronn;

Might possibly be done with a Fourier series.

ronn · 2014-02-22 22:59:47

Are you joking? How can you even think what you are writing is helpful in solving the problem?

bobbym · 2014-02-22 23:13:02

Are you joking? How can you even think what you are writing is helpful in solving the problem?

Hmmm, that is kind of harsh and even rude.

You come in posting homework in violation of this rule

http://www.mathisfunforum.com/viewtopic.php?id=14654

You show no work, no initiative of your own. When I ask you what you get when you use Parsevals I get no answer.
For your information a Fourier series is a method to sum some series. Please be polite in your replies to any member I was trying to help.

Whether you are in here as ronn or ffd please read the rules

http://www.mathisfunforum.com/misc.php?action=rules

especially #2 and #9.

Getting back to the sum, it is quite easy to derive the answer using Fourier series as I suggested in post #8.

You will end up with

which when x = 1 is the same as anonimnystefy's answer.

ElainaVW · 2014-02-23 02:12:18

I used m:) as you call it. I couldn't do the sum by hand. JimmyR told me that you and him worked it out pretty easily.
How about sharing it?

Last edited by ElainaVW (2014-02-23 02:13:11)

bobbym · 2014-02-23 02:14:48

Anything is easy when jimmyR is helping. Took about 10 minutes. It just so happens that it is related to something I am doing elsewhere. Look there for it.

gAr · 2014-02-23 02:20:00

Looks like we have attempted a similar problem before:
#1 and #38: http://www.mathisfunforum.com/viewtopic.php?id=16080

bobbym · 2014-02-23 02:22:47

Hi gAr;

Yes, it is done with Fourier series and works out nice and neat.

gAr · 2014-02-23 02:25:12

Hi bobbym,

Or by complex numbers and integrals.

bobbym · 2014-02-23 02:29:34

Hi;

I was reading a paper on using contour integration on sums as we do on integrals but now I can not remember where it is.

gAr · 2014-02-23 02:37:08

It's in the link I gave!

bobbym · 2014-02-23 02:40:18

Okay, I will go there.

This one here was easier than any of those.

gAr · 2014-02-23 02:53:40

Yes.

bobbym · 2014-02-23 02:57:06

I am working a bit with Agnishom on Fourier series. In a little while I will give him this sum to work on. He will enjoy it.

gAr · 2014-02-23 03:01:25

Sure he will.

bobbym · 2014-02-23 03:03:32

I am going to go offline for a bit. See you and thanks for coming in.

gAr · 2014-02-23 03:14:05

Okay, see you later.

ronn · 2014-02-23 03:25:14

Sorry bobbym about getting upset. I'm a bit stressed about having to solve this problem (among many others) within a limited time.

bobbym wrote:

Getting back to the sum, it is quite easy to derive the answer using Fourier series as I suggested in post #8.
You will end up with
which when x = 1 is the same as anonimnystefy's answer.

I don't understand how to use the Fourier series to solve the problem. I don't know what "sgn" and we are not allowed to use terms that we haven't learned to solve problems. Could you, or someone else, please show how you mean that the Fourier series can be used to solve the problem.

gAr · 2014-02-23 04:52:19

Hi,

That's one way. Did you check the link I gave too?

We end up with:

and

for positive n

Math Is Fun Forum

#1 2014-02-20 07:32:35

Sum of Fourier series

#2 2014-02-20 12:10:56

Re: Sum of Fourier series

#3 2014-02-22 04:00:32

Re: Sum of Fourier series

#4 2014-02-22 04:07:51

Re: Sum of Fourier series

#5 2014-02-22 07:37:34

Re: Sum of Fourier series

#6 2014-02-22 08:09:26

Re: Sum of Fourier series

#7 2014-02-22 08:29:58

Re: Sum of Fourier series

#8 2014-02-22 13:54:01

Re: Sum of Fourier series

#9 2014-02-22 22:59:47

Re: Sum of Fourier series

#10 2014-02-22 23:13:02

Re: Sum of Fourier series

#11 2014-02-23 02:12:18

Re: Sum of Fourier series

#12 2014-02-23 02:14:48

Re: Sum of Fourier series

#13 2014-02-23 02:20:00

Re: Sum of Fourier series

#14 2014-02-23 02:22:47

Re: Sum of Fourier series

#15 2014-02-23 02:25:12

Re: Sum of Fourier series

#16 2014-02-23 02:29:34

Re: Sum of Fourier series

#17 2014-02-23 02:37:08

Re: Sum of Fourier series

#18 2014-02-23 02:40:18

Re: Sum of Fourier series

#19 2014-02-23 02:53:40

Re: Sum of Fourier series

#20 2014-02-23 02:57:06

Re: Sum of Fourier series

#21 2014-02-23 03:01:25

Re: Sum of Fourier series

#22 2014-02-23 03:03:32

Re: Sum of Fourier series

#23 2014-02-23 03:14:05

Re: Sum of Fourier series

#24 2014-02-23 03:25:14

Re: Sum of Fourier series

#25 2014-02-23 04:52:19

Re: Sum of Fourier series

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