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w(t) = wα,β,δ(t) = √ 1 + t 1− t β(β − 2α) t + 2δ(β − α) t+ α + δ , t ∈ (−1, 1), where 0 < α < β, β 6= 2α, |δ| < β−α, and whose denominator is an arbitrary polynomial of exact degree 2 that remains positive on [−1, 1]. The subcase α = 1, β = 2/(1 + γ), −1 < γ < 0 and δ = 0 has been considered recently by M. M. Spalević, Error bounds of Gaussian quadrature formulae for one class of Bernstein-Szegő weights, Math. Comp., 82 (2013), 1037-1056.

Error estimates of Gaussian quadrature formulae with the third class of Bernstein-Szegő weights