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Genius guys can u solve this Fourier series problem

  1. Sep 28, 2006 #1
    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. jcsd
  3. Sep 28, 2006 #2

    HallsofIvy

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    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?
     
  4. Sep 28, 2006 #3

    quasar987

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    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?
     
  5. Sep 28, 2006 #4
    i have solved question 3 but plz plz tell me the hints how to solve question 1 and question 2
     
  6. Sep 28, 2006 #5

    HallsofIvy

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    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 -[itex]\pi[/itex] and [itex]\pi[/itex] will be odd. You should find that the "sine" coefficients are all 0.
     
  7. Sep 28, 2006 #6
    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 .
     
  8. Sep 28, 2006 #7
    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)
     
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