Padé approximants to certain elliptic-type functions [article]

Laurent Baratchart, Maxim Yattselev
2012 arXiv   pre-print
Given non-collinear points a_1, a_2, a_3, there is a unique compact, say Δ, that has minimal logarithmic capacity among all continua joining a_1, a_2, and a_3. For h be a complex-valued non-vanishing Dini-continuous function on Δ, we consider f_h(z) := (1/π i)∫_Δ h(t)/(t-z) dt/w^+(t), where w(z) := √(∏_k=0^3(z-a_k)) and w^+ the one-sided value according to some orientation of Δ. In this work we present strong asymptotics of diagonal Padé approximants to f_h and describe the behavior of the
more » ... ous pole and the regions of locally uniform convergence from a generic perspective.
arXiv:1205.4480v1 fatcat:efnaip5exzhrplw3oduhunawci