Fibonacci number

The Fibonacci numbers satisfy $F_0=0$, $F_1=1$, and $F_{n+1}=F_n+F_{n-1}$.

For $\varphi =(1+\sqrt{5})/2$ and $\psi =(1-\sqrt{5})/2$, the Fibonacci numbers satisfy

For nonnegative $n,m,l$,Cassini's identity is the adjacent-index special case.