- #1

Jack Jenkins

- 6

- 0

I have a series of polynomials P(n), given by the recursive formula P(n)=xP(n-1)-P(n-2) with initial values P(0)=1 and P(1)=x.

P(2)=xx-1=x

^{2}-1

P(3)=x(x

^{2}-1)-(x)=x

^{3}-2x

...

I am confident that all of the roots of P(n) lie on the real line. So for P(n), I hope to find these roots. I am particularly interested in the behavior of the roots as n approaches infinity.

Any help on this is truly appreciated. I haven't the tools to do this problem the way it needs to be done.

Jack