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Transactions of the American Mathematical Society

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The constrained coefficient problem for typically real functions

Author: George B. Leeman
Journal: Trans. Amer. Math. Soc. 186 (1973), 177-189
MSC: Primary 30A34
MathSciNet review: 0338347
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Abstract: 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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Keywords: Typically real functions, coefficient bounds, constrained extremal problems
Article copyright: © Copyright 1973 American Mathematical Society