Padé type approximants and orthogonal polynomials for Markov-Stieltjes functions (Q2640728)

This is one of the few results on what Brezinski has called Padé type approximants in which there is a real mix of some preassigned poles and some determined by interpolation. In this case the function is the Stieltjes transform of a positive measure supported on [-1,1], the preassigned poles are either 1 or -1 or have even multiplicities and lie off the interval, and the location of the free poles follows from orthogonality considerations.