A Characterization of Askey-Wilson polynomials

Maurice Kenfack Nangho, Kerstin Jordaan

We show that the only monic orthogonal polynomials $\{P_n{\}}_{n=0}^{\infty }$ that satisfy $$π(x)\mathcal{D}_{q}^2P_{n}(x)=\sum_{j=-2}^{2}a_{n,n+j}P_{n+j}(x),\; x=\cosθ,\;~ a_{n,n-2}…