View source for Askey-Wilson polynomial

===Three-term recurrence relation===
Any system of orthogonal polynomials <math>p_n(x)</math> satisfies a three-term recurrence relation of the form
:<math>
\label{9} x p_n(x)=A_n p_{n+1}(x)+B_n p_n(x)+C_n p_{n-1}(x),
</math>
where <math>p_{-1}(x):=0</math> and <math>A_{n-1}C_n>0</math>. One may also consider ''associated orthogonal polynomials'' <math>p_n(x;d)</math>, which satisfy the recurrence relation
:<math>
x p_n(x;d)=A_{n+d} p_{n+1}(x;d)+B_{n+d} p_n(x;d)+C_{n+d} p_{n-1}(x;d).
</math>
Here <math>d</math> is a positive integer or, more generally, a positive real number as long as this makes sense by analyticity in <math>n</math> of the coefficients <math>A_n,B_n,C_n</math>.