Second Hankel Determinants for the Class of Typically Real Functions

Paweł Zaprawa

Abstract and Applied Analysis, 2016, vol. 2016, issue 1

Abstract: We discuss the Hankel determinants H2(n)=anan+2-an+12 for typically real functions, that is, analytic functions which satisfy the condition Im ⁡z Im⁡f(z) ≥ 0 in the unit disk Δ. Main results are concerned with H2(2) and H2(3). The sharp upper and lower bounds are given. In general case, for n ≥ 4, the results are not sharp. Moreover, we present some remarks connected with typically real odd functions.

Date: 2016
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https://doi.org/10.1155/2016/3792367

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2016:y:2016:i:1:n:3792367

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