Strong asymptotics of Hermite–Pade approximants for the Nikishin system of Jacobi weights

The Hermite–Pade approximants for the Cauchy transforms of the Jacobi weights on one interval are considered. This system of functions forms a Nikishin system. The denominators of the approximants are known as Jacobi–Pineiro polynomials. For the case of two weights the integral representations are obtained, the weak asymptotics is investigated. For the diagonal indexes the strong asymptotics of the polynomials and the functions of the second kind is found. The classical saddle point method is used.