Let Γ be a closed oriented contour on the Riemann sphere. Let E and F be polynomials of degree n+1, with zeros respectively on the positive and negative sides of Γ. We compute the [n/n] and [n−1/n] Padé denominators at ∞ to f(z)=∫Γ1z−tdtE(t)F(t). As a consequence, we compute the nth orthogonal polynomial for the weight 1/(EF). In particular, when Γ is the unit circle, this leads to an explicit formula for the Hermitian orthogonal polynomial of degree n for the weight 1/|F|2. This complements the classical Bernstein–Szegő formula for the orthogonal polynomials of degree ≥n+1.