pn⁡(cos⁡θ)=pn⁡(cos⁡θ;a,b,c,d| q)=a-n⁢∑ℓ=0nqℓ⁢(a⁢b⁢qℓ,a⁢c⁢qℓ,a⁢d⁢qℓ;q)n-ℓ⁢(q-n,a⁢b⁢c⁢d⁢qn-1;q)ℓ(q;q)ℓ⁢∏j=0ℓ-1(1-2⁢a⁢qj⁢cos⁡θ+a2⁢q2⁢j)=a-n⁢(a⁢b,a⁢c,a⁢d;q)n⁢ϕ34⁡(q-n,a⁢b⁢c⁢d⁢qn-1,a⁢ⅇⅈ⁢θ,a⁢ⅇ-ⅈ⁢θa⁢b,a⁢c,a⁢d;q,q).