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Theb 1,b 2 coefficient body for Bieberbach-Eilenberg functions

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References

  1. D. Aharonov,On Bieberbach-Eilenberg functions, Bull. Amer. Math. Soc.76 (1970), 101–104.

    MATH  MathSciNet  Google Scholar 

  2. L. Bieberbach,Über einige Extremalprobleme im Gebiet der konformen Abbildung, Math. Ann.77 (1916), 153–172.

    Article  MathSciNet  MATH  Google Scholar 

  3. P. F. Byrd and M. D. Friedman,Handbook of Elliptic Integrals for Engineers and Scientists, 2nd ed., Springer-Verlag, Berlin, 1971.

    MATH  Google Scholar 

  4. S. Eilenberg,Sur quelques proprietés topologiques de la surface de sphère, Fund. Math.25 (1935). 267–272.

    MATH  Google Scholar 

  5. H. E. Fettis and J. C. Caslin,A Table of Complete Elliptic Integrals of the First Kind for Complex Values of the Modulus, Part I., Applied Math. Research Lab., Aerospace Research Lab., USAF, Wright-Patterson Air Force Base, Ohio, 1969.

    Google Scholar 

  6. P. R. Garabedian and M. Schiffer,The local maximum theorem for the coefficients of univalent functions, Arch. Rational Mech. Anal.26 (1967), 1–32.

    Article  MATH  MathSciNet  Google Scholar 

  7. J. A. Hummel,Lagrange multipliers in variational methods for univalent functions, J. Analyse Math.32 (1977), 222–234.

    MATH  MathSciNet  Google Scholar 

  8. J. A. Hummel and M. M. Schiffer,Variational methods for Bieberbach-Eilenberg functions and for pairs, Ann. Acad. Sci. Fenn. Ser. AI3 (1977), 3–42.

    MathSciNet  MATH  Google Scholar 

  9. IMSL,The International Mathematical and Statistical Library, IMSL Inc., Houston, Texas, 1975.

    Google Scholar 

  10. J. A. Jenkins,A general coefficient theorem, Trans. Amer. Math. Soc.77 (1954), 262–280.

    Article  MATH  MathSciNet  Google Scholar 

  11. J. A. Jenkins,Univalent Functions and Conformal Mappings, 2nd ed., Springer-Verlag, Berlin, 1965.

    Google Scholar 

  12. J. A. Jenkins and D. C. Spencer,Hyperelliptic trajectories, Ann. of Math.53 (1951), 4–35.

    Article  MathSciNet  Google Scholar 

  13. N. A. Lebedev and I. M. Milin,On the coefficients of certain classes of analytic functions, Mat. Sb.28 (1951), 359–400 (Russian).

    MathSciNet  Google Scholar 

  14. Z. Nehari,On the coefficients of Bieberbach-Eilenberg functions, J. Analyse Math.23 (1970), 297–303.

    Article  MATH  MathSciNet  Google Scholar 

  15. Chr. Pommerenke,Univalent Functions, Vandenhoeck and Ruprecht, Gottingen, 1975.

    MATH  Google Scholar 

  16. A. C. Schaeffer and D. C. Spencer,Coefficient Regions for Schlicht Functions, Amer. Math. Soc. Colloquium Publ., Vol. 35, Amer. Math. Soc., New York, 1950.

    MATH  Google Scholar 

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Research for this paper was supported in part by the National Science Foundation grant number MCS 77-01277 to the University of Maryland, College Park, Maryland. The computer time for the numerical calculations was supported through the facilities of the Computer Science Center of the University of Maryland.

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Hummel, J.A. Theb 1,b 2 coefficient body for Bieberbach-Eilenberg functions. J. Anal. Math. 33, 168–190 (1978). https://doi.org/10.1007/BF02790172

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