Big q-Jacobi polynomials

In mathematics, the big q-Jacobi polynomials P_n(x;a,b,c;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme.^[1]

Definition

The polynomials are given in terms of basic hypergeometric functions by

${\displaystyle \displaystyle P_{n}(x;a,b,c;q)={}_{3}\phi _{2}(q^{-n},abq^{n+1},x;aq,cq;q,q)}$