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A note on the singular points of the function generated by the Bergman operator of the second kind


Author: Paul Rosenthal
Journal: Proc. Amer. Math. Soc. 44 (1974), 163-166
MSC: Primary 35C15
DOI: https://doi.org/10.1090/S0002-9939-1974-0336033-8
MathSciNet review: 0336033
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Abstract: Let $ \psi = {P_2}(f)$ be Bergman's operator of the second kind, $ f(q)$ is analytic at $ q = 0$. In a previous paper [5] a theorem was obtained on the singularities of $ \psi $ when $ \psi $ was generated by a $ f(q)$ whose only singular points were poles. In this note we obtain a theorem on the singularities of $ \psi $ when $ \psi $ is generated by a $ f(q)$ whose singular points can be of more varied types.


References [Enhancements On Off] (What's this?)

  • [1] S. Bergman, Two-dimensional transonic flow patterns, Amer. J. Math. 70 (1948), 856-891. MR 10, 752. MR 0030379 (10:752g)
  • [2] -, Integral operators in the theory of linear partial differential equations, 2nd rev. ed., Ergebnisse der Math. und ihrer Grenzgebiete, Band 23, Springer-Verlag, New York, 1969. MR 39 #596. MR 0239239 (39:596)
  • [3] L. Bierberbach, Lehrbuch der Funktionstheorie. II, Teubner, Leipzig, 1931.
  • [4] P. Dienes, The Taylor series, Oxford Univ. Press, 1931.
  • [5] P. Rosenthal, On the location of the singularities of the function generated by the Bergman operator of the second kind, Proc. Amer. Math. Soc. 44 (1974), 157-162. MR 0328293 (48:6635)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0336033-8
Keywords: Hypergeometric function, singular points
Article copyright: © Copyright 1974 American Mathematical Society

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