# Proof of Plancherel for quantum

1. Oct 5, 2011

### Leumas13

So, I've been asked to show that
f(x)=Ʃn=0 [ansin(nπx/a) + bncos(nπx/a)

is equivalent to f(x)=Ʃn=-∞ cneinx/a

I'm kinda stuck. i want to turn this into the exponential form but I don't see how to condense this into a single term.

Thanks!

2. Oct 5, 2011

### Leumas13

Nevermind, Solved

Use the substitution that sinu = 0.5i (e^iu -e^-iu) and the equivalent for cosine and shift the register of the summation.

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