- #1
Fizz_Geek
- 20
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Homework Statement
Given x in the interval [0, [tex]\pi[/tex]], let [tex]\phi[/tex][tex]_{0}[/tex](x) = 1, and [tex]\Phi[/tex][tex]_{n}[/tex] (x) = sin ((2n-1)x).
Show that there are constants:
{A[tex]_{n}[/tex]}[tex]^{n=0}_{\infty}[/tex] and {B[tex]_{n}[/tex]}[tex]^{n=0}_{\infty}[/tex]
such that:
[tex]\sum[/tex][tex]^{n=0}_{\infty}[/tex]A[tex]_{n}[/tex][tex]\phi[/tex][tex]_{n}[/tex]=[tex]\sum[/tex][tex]^{n=0}_{\infty}[/tex]B[tex]_{n}[/tex][tex]\phi[/tex][tex]_{n}[/tex]
But A[tex]_{n}[/tex] [tex]\neq[/tex] B[tex]_{n}[/tex] [tex]\forall[/tex]n
All the n's should be subscripts. None are powers.
Relevant equations
I really don't know where to start. Any push in the right direction would be greatly appreciated.