 Askey–Wilson polynomials are the special case of Macdonald polynomials (or Koornwinder polynomials) for the non-reduced affine root system of type ("C", "C"1), and their 4 parameters "a", "b", "c", "d" correspond to the 4 orbits of roots of this root system.They are defined by 
where "ϕ" is a basic hypergeometric function and "x" = cos(θ) and (,,)"n" is the q-Pochhammer symbol.Askey–Wilson functions are a generalization to non-integral values of "n".