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A Poisson integral formula for the ellipse and some applications


Author: W. C. Royster
Journal: Proc. Amer. Math. Soc. 15 (1964), 661-670
MSC: Primary 30.35
DOI: https://doi.org/10.1090/S0002-9939-1964-0203036-7
MathSciNet review: 0203036
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References [Enhancements On Off] (What's this?)

  • [1] E. T. Copson, An introduction to the theory of functions of a complex vairable, Clarendon Press, Oxford, 1935.
  • [1] E. T. Copson, An introduction to the theory of functions in a complex variable, Oxford, 1935.
  • [2] W. C. Royster, Convexity and starlikeness of analytic functions, Duke Math. J. 19 (1952), 447-457. MR 0050012 (14:261b)
  • [3] -, Functions having positive real part in an ellipse, Proc. Amer. Math. Soc. 10 (1959), 266-269. MR 0105511 (21:4251)
  • [4] -, Coefficient problems for functions regular in an ellipse, Duke Math. J. 26 (1959), 361-372. MR 0107008 (21:5736)
  • [5] J. L. Walsh, Note on the orthogonality of Tchebycheff polynomials on confocal ellipses, Bull. Amer. Math. Soc. 40 (1934), 84-88. MR 1562802

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DOI: https://doi.org/10.1090/S0002-9939-1964-0203036-7
Article copyright: © Copyright 1964 American Mathematical Society

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