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On a criterion of rationality for a series in orthogonal polynomials

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We present a criterion of rationality for a function determined by its expansion in a series in orthogonal polynomials. This criterion can be regarded as an analog of the well-known Kronecker criterion of rationality for functions given by power series.

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References

  1. L. Kronecker, “Zur Theorie der Elimination einer Variabeln aus zwei algebraischen Gleichungen,” Monatsber. Koniglich Preuss. Akad. Wiss. Berlin, 535–600 (1881).

  2. V. I. Buslaev and S. F. Buslaev, “On the Hadamard formulas for the ellipses of meromorphy,” in: Proc. of the Institute of Mathematics of the Ukrainian National Academy of Sciences [in Russian], 5, No. 1, 1–8 (2008).

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  4. P. K. Suetin, Classical Orthogonal Polynomials [in Russian], Fizmatlit, Moscow (2007).

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  5. V. I. Buslaev, “On the analog of the Hadamard formula for the first ellipse of meromorphy,” Mat. Zametki, 85, No. 4, 552–568 (2009).

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 8, pp. 1139–1144, August, 2010.

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Buslaev, V.I. On a criterion of rationality for a series in orthogonal polynomials. Ukr Math J 62, 1326–1332 (2011). https://doi.org/10.1007/s11253-011-0432-0

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  • DOI: https://doi.org/10.1007/s11253-011-0432-0

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