Rational approximation of Markov functions generated by Borelean power-type measures

Asymptotic behavior of Pade table rows for Markov functions $\widehat{\mu}(z)$ generated by Borelean power-type measures is found. This enabled us to find sharp decreasing orders of the best approximations of $\widehat{\mu}(z)$ by rational functions with fixed number of poles. The obtained theorems supplement the known results of A.A. Gonchar, T. Ganelius, H. Stahl, D. Braess, A.A. Pekarskii, E.A. Rovba dealing with research of approximating properties of Markov functions.