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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The constrained coefficient problem for typically real functions
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by George B. Leeman PDF
Trans. Amer. Math. Soc. 186 (1973), 177-189 Request permission


Let $- 2 \leq c \leq 2$. In this paper we find the precise upper and lower bounds on the nth Taylor coefficient ${a_n}$ of functions $f(z) = z + c{z^2} + \Sigma _{k = 3}^\infty {a_k}{z^k}$ typically real in the unit disk for $n = 3,4, \cdots$. In addition all the extremal functions are identified.
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 186 (1973), 177-189
  • MSC: Primary 30A34
  • DOI:
  • MathSciNet review: 0338347