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Padé approximants to certain elliptic-type functions

Abstract : Given non-collinear points a_1, a_2, a_3, there is a unique compact, say \Delta, 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 \Delta, we consider f_h(z) := (1/\pi i)\int_\Delta h(t)/(t-z) dt/w^+(t), where w(z) := \sqrt{\prod_{k=0}^3(z-a_k)} and w^+ the one-sided value according to some orientation of \Delta. 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.
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Contributor : Laurent Baratchart <>
Submitted on : Wednesday, December 12, 2012 - 4:57:42 PM
Last modification on : Thursday, August 22, 2019 - 2:44:01 PM

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Laurent Baratchart, Maxim Yattselev. Padé approximants to certain elliptic-type functions. Journal d'analyse mathématique, Springer, 2013, 121 (1), pp.31-86. ⟨10.1007/s11854-013-0027-9⟩. ⟨hal-00764314⟩



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