
doi: 10.4064/ap83-1-10
The special class of ``concave'' functions denoted by Co(\(p\)) consists of functions \(f(z)\) which are analytic in the unit disc \(D\) except for a simple pole at \(p\), \(0 0\) for all \(z \in D\), \(P(0) = 1\), and \(P(p) = (1 + p^2)/(1 - p^2)\). The author introduces a representation of \(P(z)\) in terms of a function \(\omega(z)\) analytic in \(D\) with \(\omega(D) \subset \overline D\). A very clever method of chasing coefficients then completes the proof. As the author observes, this simple representation seems to offer an opening into proving the conjecture in general.
Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.), Coefficient problems for univalent and multivalent functions of one complex variable, concave univalent functions, Livingston conjecture
Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.), Coefficient problems for univalent and multivalent functions of one complex variable, concave univalent functions, Livingston conjecture
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