Orthogonalization of polynomial

Hi guys.

I have the following base for :

I want to orthogonalize this base with respect to the inner product:

somthing doesn't add up, and I suspect that I have made some calculation error, even though I checked several times.

so let's say the new orthogonal base will be

I first set .

then:

(I checked it - it is correct, since it's orthogonal to , which is 1)

but when I try to find , I get:

so this is what I get, but is NOT orthogonal to neither or !

any help would be greatly appreciated!

Re: Orthogonalization of polynomial

In your expression for the and (wherever they appear), on the RHS should be and shouldn't they ?

(You got lucky with because

Re: Orthogonalization of polynomial

Hi BobP, and thanks for the help.

I don't see why does it matter if I take , or , .

both , and , spans the same vector space, so if a vector is orthogonal to , , it will be orthogonal to , as well.

nevertheless, I tried to take instead, and this is what I get:

which is still not orthogonal to / / /

Re: Orthogonalization of polynomial

The formula that you have for comes from the assumption that

To calculate the coefficient (for example) you take the inner product of this equation with

That gets you

from which

That doesn't happen if you use rather than since are not orthogonal.

For the last bit, check your integration.

I get

Re: Orthogonalization of polynomial

Great! Thank you so much.

Re: Orthogonalization of polynomial

Actually, I made a mistake !

I should have put

That changes the next two lines. You get the drift though ?

Re: Orthogonalization of polynomial

yeah, I'll get it from here. thanks.