Finding roots to a recursively defined polynomial of degree n
Hi everyone, sorry for the long delay I had the flu!
All better now. I actually managed to get a directed study at my college approved that looks into this problem. What I'm concentrating on are the fact that certain numbers, such as 1, sqrt(2), sqrt(3), and (1+sqrt(5))/2 (the golden ratio) all have the property that the recursive formula P(n)=n*P(n-1)-P(n-2); P(0)=1 and P(1)=n, when n is substituted in for one of these certain numbers (which turn out to be the roots of one or more of the polynomials being discussed in this section), cause P to repeat itself, as in 1,sqrt(2),1,0,-1,-sqrt(2),-1,0,1,sqrt(2),...
Anyway, since I'm going to be doing work on this subject for legit college credit, I'm going to ask that people please keep their work on this to themselves, or at least off this page, for legal reasons. Those who have already given valuable input on this page will be credited; I will contact you personally when the time comes.