Transactions of the American Mathematical Society

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

 

 

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1973-0338347-8
Keywords: Typically real functions, coefficient bounds, constrained extremal problems
Article copyright: © Copyright 1973 American Mathematical Society