Thread: orthogonal polynomials and the recurrence relation

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!

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.