# Genius guys can u solve this Fourier series problem

1. Sep 28, 2006

### installer2001

HEllo ,
Plz help me in solving these problems regarding Fourier Series:

1):Find Fourier Sine Series for f(x)=x^2 -Π(pie)<x<Π(pie)
and deduce Π^2/12=1-1/4+1/9-1/16 +-------------------

Π indicates PIE

2):With the help of fourier Sine series and Fourier Cosine series
f(x)=x+1 0<x<Π(pie)
Deduce 1-1/3+1/5-1/7 --------------------- = Π(pie)/4
and 1+1/(3^2)+1/(5^2)+1/(7^2)--------= Π^2/8

3);Find the fourier Sine series for function f(x) =e^x 0<x<Π(pie)

2. Sep 28, 2006

### HallsofIvy

Staff Emeritus
Even the genius guys aren't going to do your homework for you. What have you done on this and where do you have a problem?

3. Sep 28, 2006

### quasar987

what the hell does Π mean!?!?!? (kidding)

1: are you sure the problem wants you to develop as a series of sine and not sosines?

4. Sep 28, 2006

### installer2001

i have solved question 3 but plz plz tell me the hints how to solve question 1 and question 2

5. Sep 28, 2006

### HallsofIvy

Staff Emeritus
The reason quasar987 asked if you are sure that a sine series is wanted rather than cosine is because x2 is a even function while sine functions are all odd and any function represented as a sine series between -$\pi$ and $\pi$ will be odd. You should find that the "sine" coefficients are all 0.

6. Sep 28, 2006

### installer2001

Well HallsofIvy my teacher gave me these 3 questions to solve and they did'nt tell anything regarding these questions and also told srudents that these questions are very important from EXAM's POINT Of VIEW. Plz plz solve this .

7. Sep 28, 2006

### installer2001

U guys r really genius & gr8. Well i consulted with my class fellow and they told me that tha real question is
1):Find Fourier Series for f(x)=x^2 -Π(pie)<x<Π(pie)
and deduce Π^2/12=1-1/4+1/9-1/16 +-------------------

Π indicates PIE

2):With the help of fourier SIne series
and Fourier Cosine series
f(x)=x+1 0<x<Π(pie)
Deduce 1-1/3+1/5-1/7 --------------------- = Π(pie)/4
and 1+1/(3^2)+1/(5^2)+1/(7^2)--------= Π^2/8

3);Find the fourier Sine series for function f(x) =e^x 0<x<Π(pie)