One quadrature formula (Q1589186)

The author studies the following quadrature formula for different classes of functions: \[ \int^1_{-1} {f(\tau)d \tau\over \sqrt{1-\tau^2}}= {\pi\over n}\sum^{n-1}_{k=1} f(\tau_k)+ {\tau\over 2n}\bigl(f(\tau_0)+ f(\tau_n)\bigr)+ R_n(f), \] where \(\tau_k= \cos{k\pi\over n}\) and \(R_n(f)\) is the remainder.