PADE APPROXIMANTS TO CERTAIN ELLIPTIC-TYPE FUNCTIONS

Among all continua joining non-collinear points a (1), a (2), a (3) a a",, there exists a unique compact Delta aS, a", that has minimal logarithmic capacity. For a complex-valued non-vanishing Dini-continuous function h on Delta, we define , f(h)(z) := 1/pi i Z1h(t)t-zdtw+(t), where and w (+) is the one-sided value according to some orientation of 1. In this work, we present strong asymptotics of diagonal Pad, approximants to f (h) and describe the behavior of the spurious pole and the regions of locally uniform convergence from a generic perspective.