# Inequality proof

#### Townsend

Show that for each complex sequence $$c_1, c_2, ..., c_n$$ and for each integer $$1 \leq H < N$$ one has the inequality

$$| \sum_{n=1}^N c_n|^2 \leq \frac{4N}{H+1} ( \sum_{n=1}^N |c_n|^2 + \sum_{h=1}^H | \rho_N(h)|)$$

Any one.....matt grime perhaps?

note: if anyone actually wants to work this out let me know and I will fill in the missing parts...but don't ask me to do it.... :tongue2:

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#### honestrosewater

Gold Member
Yeah, that's good. The more fancy meaningless symbols, the better.

#### Townsend

honestrosewater said:
Yeah, that's good. The more fancy meaningless symbols, the better.
There is an important part missing but it is a true bound...not just meaningless...

#### honestrosewater

Gold Member
Okay, I'll take your word for it. It would be nice if someone were around to explain it to me.

#### Townsend

honestrosewater said:
Okay, I'll take your word for it. It would be nice if someone were around to explain it to me.
Yeah...it would take a really smart....creative....mathematician to do so...who would be able to do that I wonder??????

#### honestrosewater

Gold Member
Townsend said:
Yeah...it would take a really smart....creative....
... and patient. I've never even worked with complex numbers before. You can just treat them as ordered pairs of real numbers, right? I think I'd like that approach.

#### Johnny5

I know the solution, but I won't say to give other people a chance. It's not that hard.

#### wolram

Gold Member
Its packman eating flies, so the ansewer must be MxBxHs

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