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New explicit formulas for the coefficients of $ p$-symmetric functions


Author: Pavel G. Todorov
Journal: Proc. Amer. Math. Soc. 77 (1979), 81-86
MSC: Primary 30C45
DOI: https://doi.org/10.1090/S0002-9939-1979-0539635-3
MathSciNet review: 539635
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Abstract: In comparison with Goodman's well-known method and results, we use an alternate method by which we obtain more tractable formulas for the coefficients of p-symmetric univalent functions of classes $ {S^p}$ and $ {\Sigma ^p}$ in terms of the coefficients of their associated functions in the class s. Our method and results are simple and convenient and they make it easier to compute the coefficients for functions in the classes $ {S^p}$ and $ {\Sigma ^p}$, because we obtain a new recursion formula for them.


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

  • [1] A. W. Goodman, Coefficients for the area theorem, Proc. Amer. Math. Soc. 33 (1972), 438-444. MR 0291437 (45:530)
  • [2] Faà di Bruno, Sullo sviluppo delle funzioni, Ann. di Sci. Mat. Fis. (Tortoloni) 6 (1855), 479-480.
  • [3] -, Note sur une nouvelle formule de calcul différentiel, Quart. J. Math. 1 (1857), 359-360.
  • [4] Charles Jordan, Calculus of finite differences, Chelsea, New York, 1965. MR 0183987 (32:1463)
  • [5] J. Riordan, An introduction to combinatorial analysis, Wiley, New York-London, 1958. MR 0096594 (20:3077)
  • [6] L. Comtet, Advanced combinatorics. The art of finite and infinite expansion, Reidel, Dordrecht and Boston, Mass., 1974. MR 0460128 (57:124)

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DOI: https://doi.org/10.1090/S0002-9939-1979-0539635-3
Article copyright: © Copyright 1979 American Mathematical Society

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