Asymptotics of the second kind polynomials and above and below point estimates of its derivatives

Above and below point estimates have been established for fixed order $j\in\mathbf Z_+$ derivatives of the second kind polynomials associated with polynomials orthogonal on the circle $|z|=1$ with respect to the weight $|\sin\tau|$. Besides the uniform asymptotical representation has been obtained for the afore mentioned second kind polynomials in terms of the ones of the first kind. This result implies the asymptotical formula for the second kind Legendre polynomials, which is an analogue of the corresponding Szegö formula for Jacobi polynomials.