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## Main Question or Discussion Point

Why is the math in the red box necessary? According to this definition, it isn't:

- Thread starter ainster31
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Why is the math in the red box necessary? According to this definition, it isn't:

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tiny-tim

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sorry, i don't understand your question …Why is the math in the red box necessary? According to this definition, it isn't:

the red box proves that (φ

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According to definition 12.1.3, a set of real-valued functions can be proven to be orthogonal if (φhi ainster31!

sorry, i don't understand your question …

the red box proves that (φ_{0}, φ_{n}) = 0 (for n ≠ 0)

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So you're saying it was unnecessary?m=0 is contained as a particular case for arbitrary m and n. It's no need to make the particular case.

That went over my head.The proof goes directly by putting cos a = Re (e^ia).

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tiny-tim

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because φAccording to definition 12.1.3, a set of real-valued functions can be proven to be orthogonal if (φ_{m}, φ_{n}) = 0. So why is it necessary to prove (φ_{0}, φ_{n}) = 0?

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That's exactly what I meant.So you're saying it was unnecessary?[...]

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