Second Hankel Determinants for the Class of Typically Real Functions

Abstract EN

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 Imf(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.