Let a> left bracketing bar b right bracketing bar , and write h(θ) = (a cos θ + b)/(2sin θ). Then define P_n(x;a, b) by the generating function f(x, w) = f(cos θ, w) = sum_(n = 0)^∞ P_n(x;a, b) w^n = (1 - w e^(i θ))^(-1/2 + i h(θ)) (1 - w e^(i θ))^(-1/2 - i h(θ)). The generating function may also be written f(x, w) = (1 - 2x w + w^2)^(-1/2) exp[(a x + b) sum_(m = 1)^∞ w^m/m U_(m - 1)(x)], where U_m(x) is a Chebyshev polynomial of the second kind.