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.
References
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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