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Univalence of Gaussian and confluent hypergeometric functions


Authors: Sanford S. Miller and Petru T. Mocanu
Journal: Proc. Amer. Math. Soc. 110 (1990), 333-342
MSC: Primary 33A30; Secondary 30C45
DOI: https://doi.org/10.1090/S0002-9939-1990-1017006-8
MathSciNet review: 1017006
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Abstract: Conditions are determined for the univalence convexity and starlikeness of Gaussian and confluent hypergeometric functions. In addition, subordination results are obtained for these classes of functions.


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

  • [1] B. C. Carlson and D. B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984), 737-745. MR 747433 (85j:30014)
  • [2] L. De Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137-152. MR 772434 (86h:30026)
  • [3] E. Kreyszig and J. Todd, The radius of univalence of the error function, Numer. Math. 1 (1959), 78-89. MR 0101918 (21:724)
  • [4] -, On the radius of univalence of the function $ \exp ({z^2})\smallint _0^2\exp ( - {t^2})dt$, Pacific J. Math. 9 (1959), 123-127. MR 0107032 (21:5759)
  • [5] -, The radius of univalence of Bessel functions, Illinois J. Math. 4 (1960), 143-149. MR 0110827 (22:1695)
  • [6] E. P. Merkes and W. T. Scott, Starlike hypergeometric functions, Proc. Amer. Math. Soc. 12 (1961), 885-888. MR 0143950 (26:1499)
  • [7] S. S. Miller and P. T. Mocanu, Differential subordinations and inequalities in the complex plane, J. Differential Equations 67 (1987), 199-211. MR 879693 (88d:30032)
  • [8] St. Ruscheweyh and V. Singh, On the order of starlikeness of hypergeometric functions, J. Math. Anal. Appl. 113 (1986), 1-11. MR 826655 (87d:30018)
  • [9] G. Sansone and J. Gerretsen, Lectures on the theory of functions of a complex variable, Vol. II, Wolters-Noordhoof Publishing, Groningen, The Netherlands, 1969. MR 0259072 (41:3714)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1017006-8
Keywords: Gaussian and confluent hypergeometric functions, univalent, convex, starlike, differential subordination
Article copyright: © Copyright 1990 American Mathematical Society

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