orthogonal polynomials and the recurrence relation

Quote:

Let

be an inner product on the real vector space of polynomials, and consider the set

of monic orthogonal polynomials defined recursively by

and

for

,

where

, and

.

Show that

.

I've been wrestling with this for several days, but I can't crack it. I don't think it's supposed to be difficult though. I suspect I'm just missing something obvious.

Any help would be much appreciated!

Re: orthogonal polynomials and the recurrence relation

Just a guess but it could be a special polynomial such as Legendre, Chebshev, etc. Look into those, because I don't remember what they look like.