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## #1 2013-08-16 01:57:24

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### n th derivative

the problem is to prove that -∫(-1 to 1) u^(n-1)(x) u^(n+1)(x)dx = (-1)^n ∫(-1 to 1)u(x)u^(2n)(x)dx
here (n-1),(n+1),(2n) are n th derivatives and u(x) = (x²-1)^n
plz help me to prove above problem...

## #2 2013-08-16 02:29:11

bobbym

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### Re: n th derivative

Hi;

You should latex these so they are readable.

This is a good online latex creator. It uses pull down menus and produces perfect latex every time.

http://latex.codecogs.com/editor.php

That is the LHS of your question. Refresh my memory, which polynomials are u(x)?

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #3 2013-08-22 02:43:01

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### Re: n th derivative

that problem u interpreted is correct, and u(x)=\left(x^2-1)^n

## #4 2013-08-22 05:27:53

bobbym

Online

### Re: n th derivative

Hi;

So the whole question looks like this:

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.