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#1 2013-08-15 03:57:24

maths4prasad
Member
Registered: 2013-08-15
Posts: 3

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...

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#2 2013-08-15 04:29:11

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,636

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#3 2013-08-21 04:43:01

maths4prasad
Member
Registered: 2013-08-15
Posts: 3

Re: n th derivative

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

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#4 2013-08-21 07:27:53

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,636

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.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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