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Fourier series

  • #1

Homework Statement


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]
 

Answers and Replies

  • #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]
 
  • #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])
 
  • #4
Defennder
Homework Helper
2,591
5
I'm not sure what you're writing here, is it [tex]\lambda \pi[/tex] or [tex]\lambda^{\pi}[/tex] ?
 
  • #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
 
  • #6
Vid
401
0
Use itex instead of tex if you want math symbols to look right in the middle of a line of text.
 
  • #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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