naa a22 4500 510781314 CHVBK 20180411083248.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s11854-013-0027-9 doi (NATIONALLICENCE)springer-10.1007/s11854-013-0027-9 Padé approximants to certain elliptic-type functions [Elektronische Daten] [Laurent Baratchart, Maxim Yattselev] Among all continua joining non-collinear points a 1, a 2, a 3 ∈ ℂ, there exists a unique compact Δ ⊂ ℂ that has minimal logarithmic capacity. For a complex-valued non-vanishing Dini-continuous function h on Δ, we define $${f_h}(z): = \frac{1}{{\pi i}}\int_\Delta {\frac{{h(t)}}{{t - z}}\frac{{dt}}{{{w^ + }(t)}}} $$ , where $$w(z): = \sqrt {\prod\nolimits_{k = 0}^3 {(z - {a_k})} } $$ and w + is the one-sided value according to some orientation of 1. In this work, we present strong asymptotics of diagonal Padé approximants to f h and describe the behavior of the spurious pole and the regions of locally uniform convergence from a generic perspective. Hebrew University Magnes Press, 2013 Baratchart Laurent 2004 Route des Lucioles, BP 93 06902, Sophia-Antipolis, France aut Yattselev Maxim Department of Mathematical Sciences, Indiana University-Purdue University, 402 North Blackford Street, 46202, Indianapolis, IN, USA aut Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 121/1(2013-10-01), 31-86 0021-7670 121:1<31 2013 121 11854 https://doi.org/10.1007/s11854-013-0027-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0027-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Baratchart Laurent 2004 Route des Lucioles, BP 93 06902, Sophia-Antipolis, France aut NATIONALLICENCE 700 1- Yattselev Maxim Department of Mathematical Sciences, Indiana University-Purdue University, 402 North Blackford Street, 46202, Indianapolis, IN, USA aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 121/1(2013-10-01), 31-86 0021-7670 121:1<31 2013 121 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer