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.
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.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 .
Any help would be much appreciated!