This article is cited in 3 papers

On the Phenomenon of Spurious Interpolation of Elliptic Functions by Diagonal Padé Approximants

D. V. Khristoforov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We study diagonal Padé approximants for elliptic functions. The presence of spurious poles in the approximants not corresponding to the singularities of the original function prevents uniform convergence of the approximants in the Stahl domain. This phenomenon turns out to be closely related to the existence in the Stahl domain of points of spurious interpolation at which the Padé approximants interpolate the other branch of the elliptic function. We also investigate the behavior of diagonal Padé approximants in a neighborhood of points of spurious interpolation.

Keywords: elliptic function, diagonal Padé approximants, spurious pole, spurious interpolation, Stahl compact set, Laurent series, Riemann surface, complex Green function.

UDC: 517.53

Received: 31.03.2009
Revised: 29.10.2009

DOI: 10.4213/mzm7708

 English version: Mathematical Notes, 2010, 87:4, 564–574

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