連續q-哈恩多項式以基本超幾何函式定義：
p_n(x;a,b,c|q)=a^{-n}e^{-inu}(abe^{2iu},ac,ad;q)_n*_4\Phi_3(q^{-n},abcdq^{n-1},ae^{i{t+2u}},ae^{-it};abe^{2iu},ac,ad;q;q)
並且
x=cos(t+u)
p_n(x;a,b,c|q)=a^{-n}e^{-inu}(abe^{2iu},ac,ad;q)_n*_4\Phi_3(q^{-n},abcdq^{n-1},ae^{i{t+2u}},ae^{-it};abe^{2iu},ac,ad;q;q)
並且
x=cos(t+u)
