Most of the orthogonal polynomials that we face, for example, in Physics are generated by recurrence relations of second order.
Are there examples of orthogonal polynomials generated by higher order recurrence relations? For example, the Chebyshev polynomials of second kind are generated by
$ U_{n}(x) = 2xU_{n-1}(x)-U_{n-2}(x) $
with the initial conditions $U_0(x)=1$, $U_{-1}(x)=0$. If we modify this recurrence relation to,
$ V_{n}(x) = 2xV_{n-1}(x)-V_{n-3}(x) $
with the initial conditions $V_0(x)=1$, $V_{-2}(x)=V_{-1}(x)=0$, how could I know if the family $\{V_{n}(x)\}$ is orthogonal?
It is not clear to me whether Favard's theorem answers these questions.