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Fourier series

  1. May 18, 2008 #1
    1. The problem statement, all variables and given/known data
    if 0<[tex]\lambda[/tex]<1 and f(x) = x for 0[tex]\leq[/tex]x[tex]\leq[/tex][tex]\lambda\pi[/tex]
    and f(x) = ([tex]\lambda[/tex]/1-[tex]\lambda[/tex])([tex]\pi[/tex]-[tex]\lambda[/tex]) for [tex]\lambda[/tex][tex]\pi[/tex][tex]\leq[/tex]x[tex]\leq[/tex][tex]\pi[/tex]
     
  2. jcsd
  3. May 18, 2008 #2
    show

    f(x)=2/[tex]\pi[/tex](1-[tex]\lambda[/tex]) [tex]\sum[/tex] (sinn[tex]\lambda[/tex][tex]\pi[/tex]sinnx)/n[tex]^{2}[/tex]
     
  4. May 18, 2008 #3
    so am i right a[tex]_{0}[/tex] and a[tex]_{n}[/tex] are both 0

    so then is b[tex]_{n}[/tex] = 1/[tex]\pi[/tex] [tex]\int^{\lambda\pi}_{0}[/tex] xsin(n[tex]\pi[/tex]x/[tex]\pi[/tex]) + 1/[tex]\pi[/tex] [tex]\int[/tex] [tex]^{\pi}_{\lambda\pi}[/tex] ---- sin(n[tex]\pi[/tex]x/[tex]\pi[/tex])
     
  5. May 18, 2008 #4

    Defennder

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    Homework Helper

    I'm not sure what you're writing here, is it [tex]\lambda \pi[/tex] or [tex]\lambda^{\pi}[/tex] ?
     
  6. May 19, 2008 #5
    its ([tex]\lambda[/tex])([tex]\pi[/tex]) not powered or anything, all on the same line but came out funny sometimes, phi seem to move up a bit
     
  7. May 19, 2008 #6

    Vid

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    Use itex instead of tex if you want math symbols to look right in the middle of a line of text.
     
  8. May 26, 2008 #7
    so am i right a[tex]_{o}[/tex] and a[tex]_{n}[/tex] are both 0

    so then is b[tex]_{n}[/tex] = 1/[itex]\pi[/itex] [itex]\int^{\lambda\pi}_{0}[/itex] xsin(n[itex]\pi[/itex]x/[itex]\pi[/itex]) + 1/[itex]\pi[/itex] [itex]\int^{pi}_{\lambda\pi}[/itex] ([tex]\lambda[/tex]/1-[tex]\lambda[/tex])([itex]\pi[/itex]-x) sin(n[itex]\pi[/itex]x/[itex]\pi[/itex])

    do i work from here?
     
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