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A note on a theorem of C. L. Siegel concerning Bessel’s equation. (English) Zbl 0489.34003

MSC:
34M99 Ordinary differential equations in the complex domain
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
12H20 Abstract differential equations
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References:
[1] L. Bieberbach : Theorie der Gewöhnlichen Differentialgleichungen . Grund. der Math., Band 66, Second Edition, Springer-Verlag, Berlin, 1965. · Zbl 0124.04603
[2] W. Hayman : Meromorphic Functions . Oxford Math. Monographs, Clarendon Press, Oxford, 1964. · Zbl 0115.06203
[3] S. Hellerstein and L. Rubel : Subfields that are algebraically closed in the field of all meromorphic functions . J. Analyse Math. 12 (1964) 105-111. · Zbl 0129.29301
[4] J. Miles : Quotient representations of meromorphic functions . J. Analyse Math. 25 (1972) 371-388. · Zbl 0247.30019
[5] R. Nevanlinna : Le Théorème de Picard-Borel et la Theorie des Fonctions Méromorphes . Gauthier-Villars, Paris, 1929.
[6] S. Saks and A. Zygmund : Analytic Functions . Monografie Mat.(Engl. Transl.), Tom 28, Warsaw, 1952. · Zbl 0048.30803
[7] C.L. Siegel : Über einige Anwendungen diophantischer Approximationen. Abh . Preuss. Akad. der Wissensch., Phys.-Math. K1. 1929, Nr. 1, 58 pp. · JFM 56.0180.05
[8] C.L. Siegel ; Transcendental Numbers . Annals of Math. Studies, No. 16, Princeton University Press, Princeton, 1949. · Zbl 0039.04402
[9] E. Titchmarsh : The Theory of Functions . Second Edition, Oxford University Press, Oxford, 1939.
[10] F. Tricomi : Repertorium der Theorie der Differentialgleichungen . Springer-Verlag, Berlin, 1968. · Zbl 0159.13601
[11] G. Valiron : Lectures on the General Theory of Integral Functions . Chelsea Publ. Co., New York, 1949.
[12] G. Valiron : Fonctions Analytiques, ”Euclid” . Presses Universitaires de France, Paris, 1964. · Zbl 0055.06702
[13] H. Wittich : Neuere Untersuchungen über Eindeutige Analytische Funktionen . Ergebn. der Math., No. 8, Springer-Verlag, Berlin, 1955. · Zbl 0067.05501
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