Some sharp estimates for typically real functions
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXVII, Tome 428 (2014), pp. 81-88
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Let $T$ be the class of functions $f(z)=z+\sum^\infty_{n=r}c_nz^n$ regular and typically real in the disk $|z|<1$. Sharp estimates for the coefficients $c_3$ and $c_4$ in terms of the values $f(r)$, $0, are obtained.
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