I am trying to show, given $H_{n+1} = xH_n-nH_{n-1}$,
that $<H_n,H_n>$ = $n<H_{n-1},H_{n-1}>$.
I have the solution available to me, from which I do not understand the following:
$<H_n,H_n>$ = $<H_n,xH_{n-1}-(n-1)H_{n-2}>$ = $...$
Specifically,I am confused on how does $H_n= H_{n-1}-(n-1)H_{n-2}$?
Thanks!