The hypergeometric orthogonal polynomials defined by P_n^(λ)(x;ϕ) = (2λ)_n/(n!) e^(i n ϕ) _2 F_1(-n, λ + i x;2λ;1 - e^(-2 i ϕ)), where (x)_n is the Pochhammer symbol. The first few are given by P_0^(λ)(x;ϕ) | = | 1 P_1^(λ)(x;ϕ) | = | 2(λ cos ϕ + x sin ϕ) P_2^(λ)(x;ϕ) | = | x^2 + λ^2 + (λ^2 + λ - x^2) cos(2ϕ) + (1 + 2λ) x sin(2ϕ).

Josef Meixner