Discrete Wronskian
= Discrete Wronskian
{title2=$W_n=p_nq_{n+1}-p_{n+1}q_n$}
= Casoratian
{c}
{synonym}
For two solutions of the <linear recurrence relation> $x_{n+2}+b_nx_{n+1}+c_nx_n=0$, their discrete <Wronskian> obeys $W_{n+1}=c_nW_n$. Substitute the recurrence into $p_{n+1}q_{n+2}-p_{n+2}q_{n+1}$: the $b_n$ terms cancel and the remaining expression is $c_n(p_nq_{n+1}-p_{n+1}q_n)$. Iteration gives $W_{n+1}=W_1\prod_{m=1}^nc_m$, including when some $c_m$ vanish. A nonzero discrete Wronskian proves <linear independence> of the two solutions.