Q-Racah polynomials

In mathematics, the q-Racah polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by. give a detailed list of their properties.

Definition
The polynomials are given in terms of basic hypergeometric functions and the Pochhammer symbol by
 * $$p_n(q^{-x}+q^{x+1}cd;a,b,c,d;q) = {}_4\phi_3\left[\begin{matrix} q^{-n} &abq^{n+1}&q^{-x}&q^{x+1}cd\\

aq&bdq&cq\\ \end{matrix};q;q\right]$$ They are sometimes given with changes of variables as
 * $$W_n(x;a,b,c,N;q) = {}_4\phi_3\left[\begin{matrix} q^{-n} &abq^{n+1}&q^{-x}&cq^{x-n}\\

aq&bcq&q^{-N}\\ \end{matrix};q;q\right]$$

Relation to other polynomials
q-Racah polynomials→Racah polynomials