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Matematicheskie Zametki, 2009, Volume 85, Issue 4, Pages 552–568
DOI: https://doi.org/10.4213/mzm5183 (Mi mzm5183) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Analog of the Hadamard Formula for the First Ellipse of Meromorphy

V. I. Buslaev

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (505 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm5183
Abstract: Suppose that Pn are orthonormal polynomials on the closed interval [−1,1] which are constructed from a weight function satisfying the Szegö condition. In this paper, we obtain the first ellipse of meromorphy of the function F(z)=∑∞n=0FnPn(z), i.e., the maximal ellipse with foci at the points ±1 to which the function F can be extended as a meromorphic function having at most one pole.
Keywords: meromorphic function, holomorphic function, pole, ellipse of meromorphy, Cauchy–Hadamard formula, Szegö condition, rational function.
Received: 17.06.2008
Revised: 04.09.2008
English version:
Mathematical Notes, 2009, Volume 85, Issue 4, Pages 528–543
DOI: https://doi.org/10.1134/S0001434609030249
Bibliographic databases:
Document Type: Article
UDC: 512.537
Language: Russian
Citation: V. I. Buslaev, “Analog of the Hadamard Formula for the First Ellipse of Meromorphy”, Mat. Zametki, 85:4 (2009), 552–568; Math. Notes, 85:4 (2009), 528–543
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm/v85/i4/p552
    • This publication is cited in the following 1 articles:
    1. Buslaev V.I., “On a criterion of rationality for a series in orthogonal polynomials”, Ukrainian Math. J., 62:8 (2011), 1326–1332  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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